Current Electricity — JEE Advanced · 2017 · 21 May 2017 · Paper 2 Question with Solution

Passage

Consider a simple RC circuit as shown in Figure 1.
Process 1: In the circuit the switch S is closed at

t = 0

and the capacitor is fully charged to voltage

V_{0}

(i.e., charging continues for time

T ≫ R C

). In the process some dissipation

(E_{D})

occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is

E_{C}

.

Process 2: In a different process the voltage is first set to

\frac{V _{0}}{3}

and maintained for a charging time

T ≫ R C

. Then the voltage is raised to

\frac{2 V _{0}}{3}

without discharging the capacitor and again maintained for a time

T ≫ R C

. The process is repeated one more time by raising the voltage to

V_{0}

and the capacitor is charged to the same final voltage

V_{0}

as in Process 1.

These two processes are depicted in Figure 2.

Consider a simple

R C

circuit as shown in Figure 1.

Process 1: In the circuit the switch

S

is closed at

t = 0

and the capacitor is fully charged to voltage

V_{0}

(i.e., charging continues for time

T ≫ R C

). In the process some dissipation

(E_{D})

occurs across the resistance

R

. The amount of energy finally stored in the fully charged capacitor is

E_{C}

.

Process 2: In a different process the voltage is first set to

\frac{V _{0}}{3}

and maintained for a charging time

T ≫ R C

. Then the voltage is raised to

\frac{2 V _{0}}{3}

without discharging the capacitor and again maintained for a time

T ≫ R C

. The process is repeated one more time by raising the voltage to

V_{0}

and the capacitor is charged to the same final voltage

V_{0}

as in Process 1.

These two processes are depicted in Figure 2.

In Process 2, total energy dissipated across the resistance

E_{D}

is:

Answer: (C)

Solution

When a capacitor is charged from

V_{i}

V_{f}

, heat dissipated is

H = \frac{1}{2} C (V_{f} - V_{i})^{2}

. Total heat in Process 2:

E_{D} = \frac{1}{2} C [(\frac{V _{0}}{3})^{2} + (\frac{V _{0}}{3})^{2} + (\frac{V _{0}}{3})^{2}] = \frac{1}{2} C \cdot 3 \cdot \frac{V _{0}^{2}}{9} = \frac{1}{6} C V_{0}^{2} = \frac{1}{3} (\frac{1}{2} C V_{0}^{2})

JEE Advanced · 2017 · 21 May 2017 · Paper 2 · Single correct option