Question

For the given circuit, find the ratio of instantaneous voltage across the inductor when current is \(2\,\text{mA}\) and when current is \(4\,\text{mA}\).

• A. \(1.5\)
• B. \(1\)
• C. \(2\)
• D. \(1.25\)

Answer 1

The Correct Option is B

Concept: In an \(RL\) circuit, the applied voltage is shared between the resistor and the inductor. \[ V = V_R + V_L \] where \[ V_R = iR \] Thus, \[ V_L = V - iR \] Step 1: When current \(i = 2\,\text{mA}\).} \[ V_R = iR \] \[ V_R = (2\times10^{-3})(6) \] \[ V_R = 0.012\,V \] Voltage across inductor: \[ V_L = 3 - 0.012 \] \[ V_L = 2.988\,V \]
Step 2: When current \(i = 4\,\text{mA}\).} \[ V_R = (4\times10^{-3})(6) \] \[ V_R = 0.024\,V \] Voltage across inductor: \[ V_L = 3 - 0.024 \] \[ V_L = 2.976\,V \]
Step 3: Find the ratio.} \[ \text{Ratio} = \frac{2.988}{2.976} \] \[ \text{Ratio} \approx 1.004 \approx 1 \] Final Result \[ \text{Ratio} = 1 \]