Question

Assertion(A): When a charged condenser discharges through a resistor, the time taken for half the charge to be lost is always same, irrespective of the initial value of the charge.
Reason(R): The rate of decay of charge in a CR\circuit is a linear function of time.

• A. Both A and R are individually true and R is the
  correct explanation of A
• B. Both A and R are individually true but R is not
  the correct explanation of A
• C. A is true but R is false
• D. Both A and R are false

Answer 1

Answer: (C)

A is true but R is false

Decay in current in R-C circuit is

$i=i_o(1-e\frac{t}{Rc})$

$=-\frac{q}{t}=\frac{q_o}{t}(1-e\frac{t}{Rc})$ $(\because i=\frac{q}{t})$

So, always half charge to be lost is equal to e t/rc = 1/2

So it is independent of initial charge

The rate of decay of charge ix exponential function of time.