Question

For an RC series circuit $E=10volt;C=10mF;R=100\Omega$ then the pick correct statements. Switch is closed at $t=0$. (Initially capacitor was uncharged)

• A. Rate of energy storage in capacitor is maximum at $t=0\cdot 0693sec$
• B. Rate of energy storage in capacitor is maximum at $t=0\cdot 053sec$
• C. Potential across capacitor and resistor become same at $t=0\cdot 0693sec$
• D. Potential across capacitor and resistor become same at $t=0\cdot 053sec$

Answer 1

Answer: (A), (C)

The correct options are
A Rate of energy storage in capacitor is maximum at $t=0\cdot 0693sec$
C Potential across capacitor and resistor become same at $t=0\cdot 0693sec$

Time Constant $\tau =\frac{1}{RC}=\frac{1}{{10}^{-3}\times 100}=10seconds$
$V=V_{max}(1-e^{-\frac{t}{\tau }})$
Rate of Energy Storage in the capacitor is given by $CV\frac{dV}{dt}=C{V}_{max}(1-e^{-\frac{t}{\tau }})\left(\frac{V_{max}}{\tau }{e}^{-\frac{t}{\tau }}\right)$
This has maximum value when $e^{-\frac{t}{\tau }})=0.5$
Hence , $t=\frac{ln2}{\tau }=\frac{0.693}{10}=0.0693s$
Potential across Resistor $=V_{max}{e}^{-\frac{t}{\tau }}$
Potential across capacitor $=V_{max}(1-e^{-\frac{t}{\tau }})$
These 2 are equal when $e^{-\frac{t}{\tau }}=0.5$
Hence , $t=\frac{ln2}{\tau }=\frac{0.693}{10}=0.0693s$