Question 21

In the figure shown, a circuit contains two identical resistors with resistance $$R = 5\Omega$$ and an inductance with $$L = 2$$ mH. An ideal battery of 15V is connected in the circuit. What will be the current through the battery long after the switch is closed?

Long after the switch is closed ($$t \to \infty$$), an ideal inductor behaves as a short circuit: $$R_L = 0$$

The circuit consists of two identical resistors $$R$$ connected in parallel across the battery:

$$R_{\text{eq}} = \frac{R \times R}{R + R} = \frac{R}{2}$$

$$R_{\text{eq}} = \frac{5}{2} = 2.5\ \Omega$$

$$I = \frac{V}{R_{\text{eq}}} = \frac{15}{2.5} = 6\text{ A}$$

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