When connecting electrical appliances to the electrical network, only the power and efficiency of the electrical appliance itself usually matters. But when using a current source in a closed circuit, the useful power it produces is important. The source can be a generator, accumulator, battery or elements of a solar power plant. This is not of fundamental importance for calculations.

Power supply parameters

When connecting electrical appliances to the power supply and creating a closed circuit, in addition to the energy P consumed by the load, the following parameters are taken into account:

• Rob. (total power of the current source) released in all sections of the circuit;
• EMF is the voltage generated by the battery;
• P (net power) consumed by all sections of the network, except the current source;
• Po (loss power) spent inside the battery or generator;
• internal resistance of the battery;
• Efficiency of the power supply.

Attention! The efficiency of the source and the load should not be confused. If the battery coefficient in an electrical appliance is high, it may be low due to losses in the wires or the device itself, and vice versa.

More about this.

Total circuit energy

When electric current passes through a circuit, heat is generated or other work is performed. A battery or generator is no exception. The energy released on all elements, including wires, is called total. It is calculated using the formula Rob.=Ro.+Rpol., where:

• Rob. - full power;
• Ro. – internal losses;
• Rpol. – useful power.

Attention! The concept of apparent power is used not only in calculations of a complete circuit, but also in calculations of electric motors and other devices that consume reactive energy along with active energy.

EMF, or electromotive force, is the voltage generated by a source. It can only be measured in X.X mode. (idle move). When a load is connected and current appears, Uо is subtracted from the EMF value. – voltage loss inside the power supply device.

Net power

Useful is the energy released in the entire circuit, except for the power supply. It is calculated by the formula:

1. “U” – voltage at terminals,
2. “I” – current in the circuit.

In a situation in which the load resistance is equal to the resistance of the current source, it is maximum and equal to 50% of the full value.

As the load resistance decreases, the current in the circuit increases along with internal losses, and the voltage continues to fall, and when it reaches zero, the current will be maximum and limited only by Ro. This is K.Z mode. - short circuit. In this case, the loss energy is equal to the total.

As the load resistance increases, the current and internal losses fall, and the voltage rises. When reaching an infinitely large value (network break) and I=0, the voltage will be equal to the EMF. This is X..X mode. - idle move.

Losses inside the power supply

Batteries, generators and other devices have internal resistance. When current flows through them, loss energy is released. It is calculated using the formula:

where “Uо” is the voltage drop inside the device or the difference between the EMF and the output voltage.

Internal power supply resistance

To calculate losses Ro. you need to know the internal resistance of the device. This is the resistance of the generator windings, the electrolyte in the battery or for other reasons. It is not always possible to measure it with a multimeter. We have to use indirect methods:

• when the device is turned on in idle mode, E (EMF) is measured;
• when the load is connected, Uout is determined. (output voltage) and current I;
• The voltage drop inside the device is calculated:

• internal resistance is calculated:

Useful energy P and efficiency

Depending on the specific tasks, maximum useful power P or maximum efficiency is required. The conditions for this do not match:

• P is maximum at R=Ro, with efficiency = 50%;
• Efficiency is 100% in H.H. mode, with P = 0.

Obtaining maximum energy at the output of the power supply device

Maximum P is achieved provided that the resistances R (load) and Ro (electricity source) are equal. In this case, efficiency = 50%. This is the “matched load” mode.

Apart from this, two options are possible:

• Resistance R drops, the current in the circuit increases, and the voltage losses Uo and Po inside the device increase. In short circuit mode (short circuit) the load resistance is “0”, I and Po are maximum, and the efficiency is also 0%. This mode is dangerous for batteries and generators, so it is not used. The exception is welding generators and car batteries that are practically out of use, which, when starting the engine and turning on the starter, operate in a mode close to “short circuit”;
• The load resistance is greater than the internal one. In this case, the load current and power P drop, and with an infinitely large resistance they are equal to “0”. This is X.H. mode. (idle move). Internal losses in the near-C.H. mode are very small, and the efficiency is close to 100%.

Consequently, “P” is maximum when the internal and external resistances are equal and is minimal in other cases due to high internal losses during short circuit and low current in the cold mode.

The maximum net power mode at 50% efficiency is used in electronics at low currents. For example, in a telephone set Pout. microphone - 2 milliwatts, and it is important to transfer it to the network as much as possible, while sacrificing efficiency.

Achieving maximum efficiency

Maximum efficiency is achieved in the H.H. mode. due to the absence of power losses inside the Po voltage source. As the load current increases, the efficiency decreases linearly in short-circuit mode. is equal to “0”. The maximum efficiency mode is used in power plant generators where matched load, maximum useful Po and 50% efficiency are not applicable due to large losses, accounting for half of the total energy.

Load efficiency

The efficiency of electrical appliances does not depend on the battery and never reaches 100%. The exception is air conditioners and refrigerators that operate on the principle of a heat pump: cooling one radiator occurs by heating the other. If you do not take this point into account, the efficiency will be above 100%.

Energy is spent not only on performing useful work, but also on heating wires, friction and other types of losses. In lamps, in addition to the efficiency of the lamp itself, you should pay attention to the design of the reflector, in air heaters - on the efficiency of heating the room, and in electric motors - on cos φ.

Knowing the useful power of the power supply element is necessary to perform calculations. Without this, it is impossible to achieve maximum efficiency of the entire system.

Video

Consider a closed unbranched circuit consisting of a current source and a resistor.

Let us apply the law of conservation of energy to the entire circuit:

.

Because , and for a closed circuit points 1 and 2 coincide, the power of electrical forces in a closed circuit is zero. This is equivalent to the statement about the potentiality of the direct current electric field, which was already mentioned earlier.

So, in In a closed circuit, all heat is released due to the work of external forces:, or , and we again come to Ohm's law, now for a closed circuit: .

Full power the circuit is called the power of external forces, it is also equal to the total thermal power:

Useful call the thermal power released in the external circuit (regardless of whether it is useful or harmful in this particular case):

(3).

The role of electrical forces in a circuit. In the external circuit, on the load R, electric forces do positive work, and when moving a charge inside a current source, they do negative work of the same magnitude. In the external circuit, heat is released due to the work of the electric field. The work given in the external circuit is “returned” by the electric field inside the current source. As a result, all the heat in the circuit is “paid for” by the work of external forces: the current source gradually loses the chemical (or some other) energy stored in it. The electric field plays the role of a “courier”, delivering energy to the external circuit.

Dependence of total, useful power and efficiency on load resistance R .

These dependencies are obtained from formulas (1 – 2) and Ohm’s law for the complete chain:

. (4)

. (5)

You can see the graphs of these dependencies in the figure.

The total power decreases monotonically with increasing , because the current in the circuit decreases. Maximum gross power is released at , i.e. at short circuit. The current source does the maximum work per unit of time, but all of it goes to heating the source itself. The maximum apparent power is

.

The useful power has a maximum at (which you can verify by taking the derivative of function (5) and equating it to zero). Substituting into expression (5), we find the maximum useful power:

.

When connecting electrical appliances to the electrical network, only the power and efficiency of the electrical appliance itself usually matters. But when using a current source in a closed circuit, the useful power it produces is important. The source can be a generator, accumulator, battery or elements of a solar power plant. This is not of fundamental importance for calculations.

Power supply parameters

When connecting electrical appliances to the power supply and creating a closed circuit, in addition to the energy P consumed by the load, the following parameters are taken into account:

• Rob. (total power of the current source) released in all sections of the circuit;
• EMF is the voltage generated by the battery;
• P (net power) consumed by all sections of the network, except the current source;
• Po (loss power) spent inside the battery or generator;
• internal resistance of the battery;
• Efficiency of the power supply.

Attention! The efficiency of the source and the load should not be confused. If the battery coefficient in an electrical appliance is high, it may be low due to losses in the wires or the device itself, and vice versa.

More about this.

Total circuit energy

When electric current passes through a circuit, heat is generated or other work is performed. A battery or generator is no exception. The energy released on all elements, including wires, is called total. It is calculated using the formula Rob.=Ro.+Rpol., where:

• Rob. - full power;
• Ro. – internal losses;
• Rpol. – useful power.

Attention! The concept of apparent power is used not only in calculations of a complete circuit, but also in calculations of electric motors and other devices that consume reactive energy along with active energy.

EMF, or electromotive force, is the voltage generated by a source. It can only be measured in X.X mode. (idle move). When a load is connected and current appears, Uо is subtracted from the EMF value. – voltage loss inside the power supply device.

Net power

Useful is the energy released in the entire circuit, except for the power supply. It is calculated by the formula:

1. “U” – voltage at terminals,
2. “I” – current in the circuit.

In a situation in which the load resistance is equal to the resistance of the current source, it is maximum and equal to 50% of the full value.

As the load resistance decreases, the current in the circuit increases along with internal losses, and the voltage continues to fall, and when it reaches zero, the current will be maximum and limited only by Ro. This is K.Z mode. - short circuit. In this case, the loss energy is equal to the total.

As the load resistance increases, the current and internal losses fall, and the voltage rises. When reaching an infinitely large value (network break) and I=0, the voltage will be equal to the EMF. This is X..X mode. - idle move.

Losses inside the power supply

Batteries, generators and other devices have internal resistance. When current flows through them, loss energy is released. It is calculated using the formula:

where “Uо” is the voltage drop inside the device or the difference between the EMF and the output voltage.

Internal power supply resistance

To calculate losses Ro. you need to know the internal resistance of the device. This is the resistance of the generator windings, the electrolyte in the battery or for other reasons. It is not always possible to measure it with a multimeter. We have to use indirect methods:

• when the device is turned on in idle mode, E (EMF) is measured;
• when the load is connected, Uout is determined. (output voltage) and current I;
• The voltage drop inside the device is calculated:

• internal resistance is calculated:

Useful energy P and efficiency

Depending on the specific tasks, maximum useful power P or maximum efficiency is required. The conditions for this do not match:

• P is maximum at R=Ro, with efficiency = 50%;
• Efficiency is 100% in H.H. mode, with P = 0.

Obtaining maximum energy at the output of the power supply device

Maximum P is achieved provided that the resistances R (load) and Ro (electricity source) are equal. In this case, efficiency = 50%. This is the “matched load” mode.

Apart from this, two options are possible:

• Resistance R drops, the current in the circuit increases, and the voltage losses Uo and Po inside the device increase. In short circuit mode (short circuit) the load resistance is “0”, I and Po are maximum, and the efficiency is also 0%. This mode is dangerous for batteries and generators, so it is not used. The exception is welding generators and car batteries that are practically out of use, which, when starting the engine and turning on the starter, operate in a mode close to “short circuit”;
• The load resistance is greater than the internal one. In this case, the load current and power P drop, and with an infinitely large resistance they are equal to “0”. This is X.H. mode. (idle move). Internal losses in the near-C.H. mode are very small, and the efficiency is close to 100%.

Consequently, “P” is maximum when the internal and external resistances are equal and is minimal in other cases due to high internal losses during short circuit and low current in the cold mode.

The maximum net power mode at 50% efficiency is used in electronics at low currents. For example, in a telephone set Pout. microphone - 2 milliwatts, and it is important to transfer it to the network as much as possible, while sacrificing efficiency.

Achieving maximum efficiency

Maximum efficiency is achieved in the H.H. mode. due to the absence of power losses inside the Po voltage source. As the load current increases, the efficiency decreases linearly in short-circuit mode. is equal to “0”. The maximum efficiency mode is used in power plant generators where matched load, maximum useful Po and 50% efficiency are not applicable due to large losses, accounting for half of the total energy.

Load efficiency

The efficiency of electrical appliances does not depend on the battery and never reaches 100%. The exception is air conditioners and refrigerators that operate on the principle of a heat pump: cooling one radiator occurs by heating the other. If you do not take this point into account, the efficiency will be above 100%.

Energy is spent not only on performing useful work, but also on heating wires, friction and other types of losses. In lamps, in addition to the efficiency of the lamp itself, you should pay attention to the design of the reflector, in air heaters - on the efficiency of heating the room, and in electric motors - on cos φ.

Knowing the useful power of the power supply element is necessary to perform calculations. Without this, it is impossible to achieve maximum efficiency of the entire system.

Video

The power developed by the current source in the entire circuit is called full power.

It is determined by the formula

where P rev is the total power developed by the current source in the entire circuit, W;

E-uh. d.s. source, in;

I is the magnitude of the current in the circuit, a.

In general, an electrical circuit consists of an external section (load) with resistance R and internal section with resistance R0(resistance of the current source).

Replacing the value of e in the expression for total power. d.s. through the voltages on the sections of the circuit, we get

Magnitude UI corresponds to the power developed on the external section of the circuit (load), and is called useful power P floor =UI.

Magnitude U o I corresponds to the power uselessly spent inside the source, It is called loss power P o =U o I.

Thus, the total power is equal to the sum of the useful power and the loss power P ob =P floor +P 0.

The ratio of useful power to the total power developed by the source is called efficiency, abbreviated as efficiency, and is denoted by η.

From the definition it follows

Under any conditions, efficiency η ≤ 1.

If we express the power in terms of the current and resistance of the circuit sections, we get

Thus, efficiency depends on the relationship between the internal resistance of the source and the resistance of the consumer.

Typically, electrical efficiency is expressed as a percentage.

For practical electrical engineering, two questions are of particular interest:

1. Condition for obtaining the greatest useful power

2. Condition for obtaining the highest efficiency.

Condition for obtaining the greatest useful power (power in load)

The electric current develops the greatest useful power (power at the load) if the load resistance is equal to the resistance of the current source.

This maximum power is equal to half of the total power (50%) developed by the current source in the entire circuit.

Half of the power is developed at the load and half is developed at the internal resistance of the current source.

If we reduce the load resistance, then the power developed at the load will decrease and the power developed at the internal resistance of the current source will increase.

If the load resistance is zero then the current in the circuit will be maximum, this is short circuit mode (short circuit) . Almost all the power will be developed at the internal resistance of the current source. This mode is dangerous for the current source and also for the entire circuit.

If we increase the load resistance, the current in the circuit will decrease, and the power on the load will also decrease. If the load resistance is very high, there will be no current in the circuit at all. This resistance is called infinitely large. If the circuit is open, its resistance is infinitely large. This mode is called idle mode.

Thus, in modes close to a short circuit and no-load, the useful power is small in the first case due to the low voltage, and in the second due to the low current.

Condition for obtaining the highest efficiency

The efficiency factor (efficiency) is 100% at idle (in this case, no useful power is released, but at the same time, the source power is not consumed).

As the load current increases, efficiency decreases according to a linear law.

In short-circuit mode, the efficiency is zero (there is no useful power, and the power developed by the source is completely consumed within it).

Summarizing the above, we can draw conclusions.

The condition for obtaining maximum useful power (R = R 0) and the condition for obtaining maximum efficiency (R = ∞) do not coincide. Moreover, when receiving maximum useful power from the source (matched load mode), the efficiency is 50%, i.e. half of the power developed by the source is wasted inside it.

In powerful electrical installations, the matched load mode is unacceptable, since this results in a wasteful expenditure of large powers. Therefore, for electrical stations and substations, the operating modes of generators, transformers, and rectifiers are calculated so as to ensure high efficiency (90% or more).

The situation is different in weak current technology. Let's take, for example, a telephone set. When speaking in front of a microphone, an electrical signal with a power of about 2 mW is created in the device’s circuitry. Obviously, to obtain the greatest communication range, it is necessary to transmit as much power as possible into the line, and this requires a coordinated load switching mode. Does efficiency matter in this case? Of course not, since energy losses are calculated in fractions or units of milliwatts.

The matched load mode is used in radio equipment. In the case where a coordinated mode is not ensured when the generator and load are directly connected, measures are taken to match their resistances.