Q. 63.7( 30 Votes )

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.

Answer :

Concepts/Formulas Used:


Resistors in Series:


Power dissipated by a resistor:


The power dissipated by a resistor of resistance R with potential difference V across it and current I passing through it is given by:



Ohm’s law:


Potential Difference (V) across a resistor of resistance R when current I passes through it is given by Ohm’s law:



Let us find the resistance of the two bulbs.


We know that,



Hence,




(i)


In series, the net resistance is:




The current in the circuit is





The power dissipated in the first bulb:



The power dissipated in the first bulb:



(ii)


In parallel, the potential through both is V. Hence the power is the same as the rated power i.e. P1 and P2.


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