Question

In the circuit shown, the switch is closed at time $t=0$.
Which of the graphs shown below best represents the voltage across the inductor, as seen on an oscilloscope?

• A. I
• B. II
• C. III
• D. IV

Answer 1

The correct option is D IV

The given circuit is an LR circuit. The voltage across the inductor is given by $V_L=L\frac{dI}{dt}$ and the voltage across resistor is $V_R=IR$

Thus, we have $10=IR+L\frac{dI}{dt}$, with the conditions $I\left(0\right)=0$

Thus, as initial current = 0, we must have $V_R\left(0\right)=0\Rightarrow V_L\left(0\right)=10V$

as $t\to \infty$ the inductor acts as a conducting wire, i.e., $V_L\left(\infty \right)=0$

The current is exponential in LR circuit. Thus, the 3 features match for fig (IV) which is the best representation of voltage across the inductor.