Question 16

The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure. What is the value of current at $$t = 4$$ s?

image

First, recall the fundamental relation between current and charge. The electric current $$I$$ through any conductor (or here, through the leads of the capacitor) is defined as the time‐rate of change of charge $$q$$ flowing past a given point. Mathematically, the definition is

$$I \;=\;\dfrac{dq}{dt}$$

We are given a graph of charge on the capacitor plate as a function of time. The question asks for the value of the current at the particular instant $$t = 4\;\text{s}$$. From the definition above, this current is nothing but the slope of the $$q$$-versus-$$t$$ curve at that instant.

Now, observe the portion of the graph that covers the interval from $$t = 3\;\text{s}$$ to $$t = 5\;\text{s}$$. In this stretch, the plotted charge remains perfectly horizontal, indicating that the value of charge does not change with time. Expressed algebraically, during this interval we have

$$q(t) = \text{constant}$$

Since the function is constant, its derivative with respect to time is zero:

$$\dfrac{dq}{dt} = 0$$

Substituting this derivative back into the current definition, we obtain

$$I = \dfrac{dq}{dt} = 0$$

Hence, at $$t = 4\;\text{s}$$—which lies squarely in the mentioned flat region—the current through the circuit is zero.

Hence, the correct answer is Option C.

Was this solution helpful?

Get AI Help

Video Solution

video

Create a FREE account and get:

  • Free JEE Mains Previous Papers PDF
  • Take JEE Mains paper tests
Ask AI