Question

The impulse response of an RL circuit is a

• A. Rising exponential function
• B. Decaying exponential function
• C. Step function
• D. Parabolic function

Hint:

For any stable first-order RL or RC circuit, the impulse response contains \[ e^{-t/\tau} \] where \(\tau\) is the time constant. Hence the response always decays exponentially.

Answer 1

The Correct Option is B

Concept: The impulse response of a system is the output produced when a unit impulse input is applied. For an RL circuit, the transfer function has a first-order denominator, resulting in an exponentially decaying impulse response.

Step 1: Write the transfer function of an RL circuit.
For a first-order RL network, \[ H(s)=\frac{1}{Ls+R}. \] Factoring out \(L\), \[ H(s)=\frac{1/L}{s+\frac{R}{L}}. \]

Step 2: Find the inverse Laplace transform.
The impulse response is \[ h(t)=\mathcal{L}^{-1}\{H(s)\}. \] Hence, \[ h(t) = \frac{1}{L} e^{-\frac{R}{L}t}u(t). \]

Step 3: Identify the nature of the response.
The term \[ e^{-\frac{R}{L}t} \] decreases continuously with time. Therefore the impulse response is a decaying exponential. \[ \boxed{\text{Decaying exponential function}} \]