Question

A condenser in series with a resistor is connected through a switch to a battery of negligible internal resistance and having an emf of 12 V. One second after closing the switch, the condenser is found to have a potential difference of 6 V. The time constant of the system is:

• A. $2$
• B. $\frac{1}{ln2}$
• C. $ln2$
• D. $ln\left(\frac{1}{2}\right)$

Answer 1

The correct option is B $\frac{1}{ln2}$

$V_0=12V$

$V=\frac{I_o}{2}=6V$

$\therefore 6=12(1-e^{\frac{-t}{RC}})$

$e^{\frac{-t}{RC}}=\frac{1}{2}$

$e^{\frac{t}{RC}}=2$

$t\frac{1}{RC}=ln2$

$t=1Sec$

$\frac{1}{RC}=ln2$

Hence , $\tau =\frac{1}{ln2}$