Chapter 33, Problem 1OQ

To determine

The statement which is true.

Answer to Problem 1OQ

The current in the circuit immediately after the switch is closed is zero. Thus, option (c) the current in the circuit is zero is correct.

Explanation of Solution

In case of $RL$ circuit in which resistor and inductor are in series. The current in the circuit which pass through resistor and inductor are in phase with each other.

Write the expression to obtain the current in the $RL$ circuit.

    $I=I_0\left(1-e^{\frac{-Rt}{L}}\right)$

Here, current in the circuit is $I$, $I_0$ is the maximum current in the circuit, $R$ is the resistance of the resistor, $L$ is the inductance of the inductor and $t$ is the duration of time.

Substitute $0$ for $t$ in the above equation to calculate $I$.

    $\begin{array}{c}I=I_0\left(1-e^{\frac{-R\left(0\right)}{L}}\right)\\ =I_0\left(1-1\right)\\ =I_0\left(0\right)\\ =0\end{array}$

Therefore, the current in the circuit immediately after the switch is closed is zero. Thus, option (c) the current in the circuit is zero is correct.