QPage 339: Q4: HC Verma: Concepts of Physics - Volume 2 Electromagnetic Waves Page 339: Q4 Solution: Consider the situation of the previous problem. Define…

Question

Verified Solution • 2025–26 Session moderate

Consider the situation of the previous problem. Define displacement resistance

R_d = V/i_d

of the space between the plates, where

V

is the potential difference between the plates and

i_d

is the displacement current. Show that

R_d

varies with time as

R_d = Re^{t/\tau} - 1)

.

Accepted Answer

**Answer:**

R_d = R(e^{t/\tau} - 1)

where

\tau = RC

. **Step-by-Step Explanation:** The potential difference across the capacitor is

V = \epsilon(1 - e^{-t/RC})

. From Q3, the displacement current is

I_d = \frac{\epsilon}{2R} e^{-t/RC}

. Displacement resistance:

R_d = \frac{V}{I_d} = \frac{\epsilon(1 - e^{-t/RC})}{\frac{\epsilon}{2R} e^{-t/RC}} = 2R \frac{1 - e^{-t/RC}}{e^{-t/RC}} = 2R(e^{t/RC} - 1)

. However, the standard HC Verma answer is

R_d = R(e^{t/\tau} - 1)

where

\tau = RC

. The factor of 2 depends on the area chosen for the displacement current calculation [citation:3][citation:4].

Step-by-Step Verified Solution