Question

How many time constants will elapse before the current in a charging RC circuit drops to half of its initial value? Answer the same question for a discharging RC circuit.

Answer 1

The number of time constants are 0.69 in the charging RC circuit before the current in the charging RC circuit drops to half of the initial value.

Explanation:

Across a capacitor, the charge growth is

q = Q2 = Q1 – e - tRCq  

⇒Q2 = Q 1-e-tRC

⇒12 = 1-e-tRC

⇒tRC = ln 2  

Let t = nRC

⇒nRCRC = 0.69  

⇒n = 0.69

Across the capacitor, the charge decay is

q = Qe-tRCq = Q2

⇒Q2 = Qe – tRC

⇒nRCRC = ln 2

⇒n = 0.69