Electric power is the rate at which work is done or energy is transformed into an electrical circuit. Simply put, it is a measure of how much energy is used in a span of time.

**Formula**

The formula for electric power is given by

P = VI

where,

P is the power

V is the potential difference in the circuit

I is the electric current

Power can also be expressed as

P = I2R

P = V2/ R

The above two expressions are got by using Ohm’s law, Where, Voltage, current, and resistance are related by the following relation

V = IR

Where,

R is the resistance in the circuit.

V is the potential difference in the circuit

I is the electric current

### Solution

(i) When two bulbs rated (P1, V) and (P2, V) are connected in series:

The current is the same via each bulb. If R1 and R2 are resistances of two bulbs, then the effective resistance of the circuit is

R = R1 + R2

Using the relation we get

P=V2 / R and

R = V2 / P

Hence

V2 / P = V12 / P1 + V22 / P2

Given: V1 = V2 = V.

Therefore,

1/ P = 1 / P1 + 1 / P2

Thus, the effective power when two bulbs are connected in series is

1/ P = 1 / P1 + 1 / P2

(ii) When two bulbs rated (P1, V) and (P2,V) are connected in parallel

1/R = 1/R1 + 1/R2

We know that

P = V2/ R

1/R = V2/ P

Given V1 = V2

Hence

P/V2 = P1/V2 + P2/V2

Thus, the effective power when two bulbs are connected in parallel is P = P1 + P2.