Electric Power
Electric power is the rate at which work is done or energy is transformed in an electrical circuit. It is a measure of how much energy is used in a span on time.
When a current “I” flows through a conductor for a time t, work done W is given by:
W = VIt
Where,
V = Potential difference across the two ends of the conductor.
Since, Power is defined as the rate of doing work.
\(Power(P)\,\,=\,\,\frac{Work\,\,Done\,\,(W)}{time(t)}\,\,=\,\,\frac{VIt}{t}\,\,=\,\,VI\),
Power (P) = VI.
Thus, Electric Power is the product of Electric current and the Potential difference due to which the current flows.
Units of Electric Power:
Power is measured in “Watt”.
1 Watt = 1 Volt x 1 amp
Power of an electric circuit is said to be 1 Watt, if a current of 1 amp flows through it when there is a potential difference of 1 Volt across its ends.
We can measure power in “Kilowatt” also commonly used.
1 Kilowatt = 1000 Watt.
Voltage, Current and Resistance are related by the following relation:
We know that:
V = IR
Where,
R = Resistance of the Circuit.
Therefore, the Electric Power can also be calculated using the following relations:
Power (P) = I² R … (1)
Power (P) = V²/R … (2)
Since, power is the rate of energy consumption, Energy can directly be calculated using:
Power (P) = Et.
Where,
E = Energy consumption.
How to find the Electric Power?
Problem: A 10 V battery is connected to a resistor having resistance of 10Ω. What is the current and power across the resistor?
Solution:
Given,
Voltage (V) = 10V
Resistance (R) = 10Ω
We know that:
\(Current(I)\,\,=\,\,\frac{Voltage(V)}{\operatorname{Re}sis\tan ce(R)}\,\,=\,\,\frac{10V}{10\Omega }\,\,=\,\,1A\),
Now,
Power (P) = Voltage (V) x Current (I)
= 10 Volts x 1A
= 10 Watts
∴ Power (P) = 10Watts.