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Question

Two identical resistors, each of resistance 15ohm, are connected in (i) series, and (ii) parallel, in turn to a battery of 6V. Calculate the ratio of the power consumed in the combination of resistors in each case.


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Solution

Step 1: Calculation of equivalent resistance while connected in series

The equivalent resistance of the resistors when connected in series can be found as follows:

R=R1+R2R=15ohm+15ohmR=30ohm

Where R is the equivalent resistance, R1 and R2 is the resistance of the resistors.

Step 2: Calculation of equivalent resistance while connected in parallel

The equivalent resistance of the resistors when connected in parallel can be found as follows:

1R=1R1+1R21R=115ohm+115ohm1R=215ohmR=7.5ohm

Step 3: Calculation of power in both the cases

The equation of power can be expressed as follows:

P=V2R

Where, P is the power, and V is the voltage.

  1. Power while the connection is in series

Pseries=6V230ohmPseries=1.2watt

2. Power while the connection is in parallel

Pparallel=6V27.5ohmPparallel=4.8watt

3. Calculation of ratio of powers

PseriesPparallel=1.24.8PseriesPparallel=14

Therefore, the ratio of powers is 1:4.


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