#### Question

Two exactly similar electric lamps are arranged (i) in parallel, and (ii) in series. If the parallel and series combination of lamps are connected to 220 V supply line one by one, what will be the ratio of electric power consumed by them?

#### Solution

Let R be the resistance of the lamp and V be the potential difference applied.__In a series connection__:

Net resistance of the circuit, R_{1} = R + R = 2R

Power drawn, P_{1} = V^{2}/R_{1} = V^{2}/2R__In a parallel connection__:

Net resistance of the circuit, R_{2} will be:

`1/R_2=1/R+1/R=2/R` or `R_2=R/2`

Power drawn, P_{2} = V^{2}/R_{2} = 2V^{2}/R

Therefore, P_{2}:P_{1} = 4:1

Is there an error in this question or solution?

Solution Two Exactly Similar Electric Lamps Are Arranged (I) in Parallel, and (Ii) in Series. If the Parallel and Series Combination of Lamps Are Connected to 220 V Supply Line One by One, What Will Be the Ratio of Electric Power Consumed by Them? Concept: Resistance of a System of Resistors - Resistors in Parallel.