Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Current in Conductors
A capacitor C₁ of capacitance 1 F and a capacitor C₂ of capacitance 2 F are charged separately for a long time by a common battery. The two capacitors are subsequently discharged separately through equal resistors. Both of the discharge circuits are connected at t = 0 .
Options
- AThe current in each of the two discharging circuits is zero at t = 0
- BThe currents in the two discharging circuits at t = 0 are equal but non-zero
- CThe currents in the two discharging circuits at t = 0 are unequal
- DC₁ loses 50 % of its initial charge sooner than C₂ loses 50 % of its initial charge
Correct answer
D. C₁ loses 50 % of its initial charge sooner than C₂ loses 50 % of its initial charge
Step-by-step solution
Let the common battery voltage be V₀ . The initial voltage across both capacitors is V₀ . During discharge, the current at time t is given by I(t) = V₀ R e^ -t/RC . At t = 0 , the initial current in both circuits is I(0) = V₀ R . Since V₀ and R are the same for both circuits, the initial currents are equal and non-zero. The charge on a discharging capacitor at time t is q(t) = q₀ e^ -t/RC . The time t taken to lose 50 % of the initial charge is obtained by setting q(t) = 0.5 q₀ , which gives t = RC 2 . Since C₁ Thu