Electric Power Definitions, Equations and Examples

Electric Power

Electric power is defined as the rate at which electrical work is done or the rate at which electrical energy is consumed or dissipated. The power P is given by P= W/t = I2R

Watt

Watt is the unit of power and is defined as the power consumed when 1 A of current flows at a potential difference of 1 V. Thus, Electric Power in Watts = Volt ampere.
When electrical energy is consumed at the rate of 1 J per second, power consumed is said to be 1 Watt.

Kilowatt hour

A kilowatt-hour is the commercial unit of electric energy and is defined as the energy consumed when 1 KW is used for 1 hour.
1 kWh = 1 kW × 1 hour = 1000 watt × 3600 second = 3.6 × 106 joule

Electric Power Definitions, Equations and Examples

Electrical appliances are not connected in series
Different appliances need different values of current for their proper operation. Whereas, in a series circuit, the current is constant throughout the circuit. Also, when one component fails in a series circuit, the entire circuit is broken and none of the components work. On the other hand, a parallel circuit divides the current through the electrical gadgets.

Example 1.
An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the power consumed will be:
(a) 100 W
(b) 75 W
(c) 50 W
(d) 25 W
Answer:
(d) 25 W

Explanation: It is given that P = 100 W and V = 220 V. Therefore, we will first calcu¬late resistance of the bulb using the formula
R = \(\frac{V^{2}}{P}=\frac{220 \times 220}{100}\) = 484 Ohm.
When this bulb is operated on 110 V, power consumed will be
P = \(\frac{V^{2}}{R}=\frac{110 \times 110}{484}=\frac{12100}{484}\) = 25 W

Electric Power Definitions, Equations and Examples

Example 2.
Compare the power used in the 2 Ω resistor in each of the following circuits: (A) a 6 V battery in series with 1 Ω and 2 Ω resistors, and (B) a 4 V battery in parallel with 12 Ω and 2 Ω resistors.
Answer:
(A) The figure below shows a 6V battery in series with 1 Ω and 2 Ω resistors, in 2n
Electric Power Definitions, Equations and Examples 1
The total resistance in the series circuit = 1 Ω + 2 Ω = 30.
Current, I = V/R = 6/3 A = 2 A.
Power used in the 2 Ω resistor = I2R= 2 × 2 × 2 = 8W
(B) The figure below shows a 4 V battery in parallel with 12 Ω and 2 Ω resistors.
Electric Power Definitions, Equations and Examples 2
The current through the 2 Ω resistor = V/R = 4/2 = 2A (since the two resistors are connected in parallel, the potential difference across them is same). Power used = I2R = 2 × 2 × 2 = 8W.

Therefore, the power used in the 2 Ω resistors in both the circuits is the same.

Class 10 Science Notes