Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t₁ is the time taken for the energy stored in the capacitor to reduce to half its initial value and t₂ is the time taken for the charge to reduce to one-fourt

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Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t₁ is the time taken for the energy stored in the capacitor to reduce to half its initial value and t₂ is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio t₁ / t₂ will be

Quantrex Academy · Accepted Answer

Correct answer: C. 1 4

U = 1 2 q ^2 C = 1 2 C ( q ₀ e ^ - t / T )^2= q ₀^2 2 C e ^ -2 t / T ( where = CR ) U = U _ i e ^ -2 t / 1 2 U _ i = U _ i e ^ -2 t ₁ / 1 2 = e ^ -2 t ₁ / t ₁= T 2 2 Now q = q ₀ e ^ - t / T 1 4 q ₀= q ₀ e ^ - t / 2 ~T t ₂= T 4=2 T 2 t ₁ t ₂ = 1 4

Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t₁ is the time taken for the energy stored in the capacitor to reduce to half its initial value and t₂ is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio t₁ / t₂ will be

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