Question

Two metallic wires of the same material and same length have different diameters. When the wires are connected in series, the heat produced in the thinner wire is $H_1$ and that in thicker wire is $H_2$, then which of the following is true?

• A. $H_1=H_2$
• B. $H_1>H_2$
• C. $H_1<H_2$
• D. Nothing can be decided

Answer 1

The correct option is B

$H_1>H_2$

1. Heat generated due to electric current is given by: $H=I^{2}Rt$

Here, the wires are connected in a series combination. Thus, the current through them is the same for the same time.

2. Heat is directly proportional to the resistance

$\Rightarrow H\propto R$

We know that, $R=\frac{\rho L}{A}$

Here, both the wires are made up of the same material and are of the same length.

$\Rightarrow$resistivity is constant for both wires.

$\Rightarrow R\propto \frac{1}{A}$

Thus, the thinner wire has more resistance as compared to the thicker wire.

Now, from (B), $\Rightarrow H\propto R$

3. The wire with more resistance will have greater heat produced.

Therefore, the heat produced in the thinner wire is more as compared to the heat produced in the second wire.

Therefore, $H_1>H_2$

Hence, option (B) is the correct answer.