Question

Plz give me ans with explanation

Answer 1

By Joule's Law, the amount of heat produced is,

$\longrightarrow\sf{H=\dfrac{V^2t}{R}}$

where $\sf{V}$ is voltage, $\sf{R}$ is resistance and $\sf{t}$ is time taken.

The voltage is same in each circuit. So, at constant time,

$\longrightarrow\sf{H\propto\dfrac{1}{R}}$

That is, amount of heat produced is inversely proportional to effective resistance of the circuit.

Effective resistance of first circuit is,

$\longrightarrow\sf{R_1=2\ \Omega}$

Effective resistance of second circuit is,

$\longrightarrow\sf{R_2=2\ \Omega+2\ \Omega}$

$\longrightarrow\sf{R_2=4\ \Omega}$

Effective resistance of third circuit is,

$\longrightarrow\sf{R_3=\dfrac{2\ \Omega\cdot2\ \Omega}{2\ \Omega+2\ \Omega}}$

$\longrightarrow\sf{R_3=\dfrac{4\ \Omega^2}{4\ \Omega}}$

$\longrightarrow\sf{R_3=1\ \Omega}$

We see that,

$\longrightarrow\sf{R_3\ \textless\ R_1\ \textless\ R_2}$

Since $\sf{H\propto\dfrac{1}{R},}$

$\longrightarrow\sf{H_3\ \textgreater\ H_1\ \textgreater\ H_2}$

Heat produced in third circuit is maximum.

Hence (D) is the answer.