Question

A mega ohm resistor and an uncharged $1\mu F$ capacitor are connected in a single loop circuit with a constant sources of $4 volt.At one second after the connection is made what are the rates at which the charge on the capacitors is increasing:

• A. $4(1-e^{-1/3})\mu C/s$
• B. $4e^{-1/3}\mu C/s$
• C. $\frac{4}{3}{e}^{-1/3}\mu C/s$
• D. $\frac{4}{3}(1-e^{-1/3})\mu C/s$

Answer 1

The correct option is C $\frac{4}{3}{e}^{-1/3}\mu C/s$

Given, $R=3\times {10}^6\Omega ,c={10}^{-6},E=4v$

For Rc circuit, time constant $Rc=3\times {10}^6\Omega \times {10}^{-6}=3\mu C$

Because the change in the capacitor is $q=q_0(1-e^{-\frac{t}{Rc}})$

Therefore the rate of change is:

$i=\frac{dq}{dt}=\frac{q_0}{Rc}{e}^{-\frac{t}{Rc}}$

If $t=1s$

$=\frac{dq}{dt}=\frac{4}{3}\left(e^{-\frac{1}{3}}\right)\mu C$