Question

A capacitor is discharging through a resistor R. Consider in time t₁, the energy stored in the capacitor reduces to half of its initial value and in time t₂, the charge stored reduces to one eighth of its initial value. The ratio t₁/t₂ will be

• A. \(\frac{1}{2}\)
• B. \(\frac{1}{3}\)
• C. \(\frac{1}{4}\)
• D. \(\frac{1}{6}\)

Answer 1

The Correct Option is D

The correct answer is (D) : \(\frac{1}{6}\)
For a discharging capacitor when energy reduces to half the charge would become 1/√2 times the initial value.
\(⇒ ( \frac{1}{2} )^{1/2} = e^{-t1/r}\)
Similarly,
\(( \frac{1}{2} )^3 = e^{-t2/r}\)
\(⇒ \frac{t1}{t2} = \frac{1}{6}\)