The impulse response of an RL circuit refers to the output response of the circuit when an impulse signal is applied to it. An impulse signal is a short pulse with an infinite amplitude and infinitesimal duration. When this impulse signal is applied to an RL circuit, the circuit responds by generating a specific output waveform, which is known as the impulse response.

RL Circuit:

Before diving into the impulse response, let's first understand the RL circuit. An RL circuit consists of a resistor (R) and an inductor (L) connected in series or parallel. When a voltage or current is applied to the circuit, it takes some time for the current to reach its steady-state value due to the presence of inductance.

Impulse Response:

The impulse response of an RL circuit is a measure of how the circuit responds to an impulse input. It describes the behavior of the circuit over time. The impulse response may vary depending on the initial conditions of the circuit.

Decaying Exponential Function:

The correct answer is option 'D', which states that the impulse response of an RL circuit is a decaying exponential function. This means that the output waveform of the RL circuit, when an impulse signal is applied, decays over time in an exponential manner.

Explanation:

When an impulse signal is applied to an RL circuit, the inductor resists the sudden change in current. As a result, the current through the inductor increases gradually until it reaches its steady-state value. This behavior can be described by a decaying exponential function.

The decaying exponential function represents the time it takes for the inductor to reach its steady-state value. Initially, the current rises rapidly, but as time passes, the rate of change decreases, and the current approaches a constant value. This behavior is characteristic of RL circuits due to the presence of inductance.

The decaying exponential function can be mathematically represented as:

i(t) = I0 * e^(-t/τ)

where i(t) is the current at time t, I0 is the initial current, t is the time, and τ is the time constant of the circuit. The time constant depends on the values of resistance and inductance in the circuit.

In summary, the impulse response of an RL circuit is a decaying exponential function because the circuit takes time to reach its steady-state value due to the presence of inductance. The decaying exponential function represents the gradual increase in current until it reaches a constant value.