Two bulbs are rated (P1, V) and (P2, V). If they are connected (i) in series and (ii) in parallel across a supply V, find the power dissipated in the two combinations in terms of P1 and P2.
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Explanation:
Given Bulbs are rated as (P1, V) & (P2, V) respectively.
The resistance of 1st bulb, R1=V2P1
The resistance of 2nd Bulb, R2=V2P2
(i) When Both are connected in Series with a power supply of voltage V.
As both the bulbs are in series connection hence both will have the same amount of current flowing through them.
i=VR1+R2=VV2P1+V2P2=1VP1P2P1+P2
Power dissipated in the circuit,
Pd=i2(R1+R2)=1V2P1P2P1+P22V2P1+V2P2Pd=P1P2P1+P2
(ii) When both are connected in parallel
In this case, Both bulbs will get the same voltage supply.
Hence Power dissipated,
Pd=V2R1+V2R2=V2P1V2+P2V2Pd=P1+P2
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