Introduction:
A pulse of magnitude 10V is applied at time t=0 to a series R-L circuit. In this circuit, a resistor (R) and an inductor (L) are connected in series. When a voltage pulse is applied to the circuit, it causes a current to flow through the circuit. The behavior of the circuit can be analyzed by considering the response of the circuit to the applied pulse.

Response of the Circuit:
When a pulse of magnitude 10V is applied to the series R-L circuit, the circuit responds by establishing a current through the components. The response of the circuit can be divided into two phases: the transient response and the steady-state response.

Transient Response:
During the transient response, the current in the circuit is changing with time. This occurs because the inductor opposes changes in current. Initially, when the pulse is applied, the inductor acts as a short circuit due to its low impedance at high frequencies. As a result, the current rises rapidly in the circuit. However, as the current continues to increase, the inductor starts building up energy in its magnetic field, causing the opposition to the change in current. This results in a decrease in the rate of increase of current.

Steady-state Response:
After a certain amount of time, the transient response settles down, and the circuit reaches a steady-state response. In the steady-state, the current in the circuit becomes constant. The inductor now behaves as a normal inductor with a high impedance at high frequencies. The resistor, on the other hand, allows the flow of current without any opposition. As a result, the current through the circuit stabilizes and remains constant.

Equations:
The behavior of the current in the series R-L circuit can be mathematically described using the following equations:

1. Voltage across the inductor:
VL = L(di/dt)

2. Voltage across the resistor:
VR = IR

3. Ohm's Law:
VR = R * I

4. Kirchhoff's Voltage Law (KVL):
VR + VL = V

Conclusion:
In conclusion, when a pulse of magnitude 10V is applied to a series R-L circuit, the circuit responds by establishing a current. Initially, there is a transient response where the current is changing with time. Eventually, the circuit reaches a steady-state response where the current becomes constant. The behavior of the circuit can be analyzed using the equations for voltage and current in the circuit. Understanding the response of the circuit is essential in designing and analyzing various electronic systems and applications.