Question

The plates of a capacitor are charged to a potential difference of 320 volts and are then connected across a resistor. The potential difference across the capacitor decays exponentially with time. After 1 second the potential difference between the plates of the capacitor is 240 volts, then after 2 and 3 seconds the potential difference between the plates will be

• A. 200 and 180 volts
• B. 180 and 135 volts
• C. 160 and 80 volts
• D. 140 and 20 volts

Answer 1

Answer: (B)

180 and 135 volts

Answer 2

During discharging potential difference across the capacitor falls exponentially as $V = V_{0}e^{- \lambda t}$ (λ = 1/RC)

Where V = Instantaneous P.D. and $V_{0} =$max. P.D. across capacitor

After 1 second V₁ = 320 (e^–λ) ⇒ 240 = 320 (e^–λ) ⇒ $e^{- \lambda} = \frac{3}{4}$

After 2 seconds V₂ = 320 (e^–λ)² ⇒ $320 \times \left( \frac{3}{4} \right)^{2} = 180volt$

After 3 seconds V₃ = 320 (e^–λ)³ = $320 \times \left( \frac{3}{4} \right)^{3} = 135volt$