Question

The voltage across the inductor for \( t > 0 \) in the given circuit is:

• A. \( v = 25e^{\gamma t} \, \text{V} \)
• B. \( v = 25e^{-\gamma t} \, \text{V} \)
• C. \( v = -25e^{\gamma t} \, \text{V} \)
• D. \( v = -25e^{-\gamma t} \, \text{V} \)

Hint:

For an RL circuit, the voltage across the inductor decays exponentially with time, following the equation \( v_L(t) = V_0 e^{-\gamma t} \), where \( \gamma = \frac{R}{L} \).

Answer 1

The Correct Option is B

Step 1: Understand the behavior of an inductor.
In an RL circuit, the voltage across the inductor for \( t>0 \) is governed by the natural response of the inductor, given by the equation: \[ v_L(t) = V_0 e^{-\gamma t} \] where \( \gamma = \frac{R}{L} \) is the time constant.
Step 2: Apply the given values.
Here, \( V_0 = 25 \, \text{V} \), and we find that the voltage across the inductor for \( t>0 \) is: \[ v = 25e^{-\gamma t} \, \text{V} \]
Final Answer: \[ \boxed{(2) \, v = 25e^{-\gamma t} \, \text{V}} \]