Electricity And Magnitism, Resistance

Electricity and Magnetism Level 2

Two conducting wires of the same material and of equal lengths and diameter are first connected in series and then in parallel in a circuit across the same potential difference. What is the ratio of the heat dissipated in the series circuit to that dissipated in the parallel one?

1:4

1:2

2:1

4:1

2 solutions

John Carlo Perion
Aug 25, 2014

The equivalent resistance for the series connection would be:

${R}_{S}=R+R=2R$

For the parallel connection:

${R}_{S}=\frac{(R)(R)}{R+R}=\frac{R}{2}$

The heat produced by each resistors is proportional to the power dissipated by each of them so:

$\frac { { E }^{ 2 } }{ 2R } :\frac { { E }^{ 2 } }{ \frac { R }{ 2 } }$

$\boxed { 1:4 }$

Rohit Gupta
May 23, 2015

As the Potential difference is same therefore the heat dissipated is inversely proportional to the resistance..!!

Electricity And Magnitism, Resistance

2 solutions

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