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-four

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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 (q₀ e^ -t / T )^2= q₀^2 2 C e^ -2 t / T (where = CR )U=U₁ e^ -2 t₁ / 1 2 U₁=U₁ e^ -2 t₁ / ; 1 2 =e^ -2 t₁ / t₁= T 2 2 Now, q=q₀ e^ -t / T aligned & 1 4 q _ o = q _ o e ^ - t / 2 ~T & t ₂= T 4=2 T 2 & t ₁ t ₂ = 1 4 aligned

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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