Question

In an oscillating $L-C$ circuit in which $C=4.00\mu F$, the maximum potential across the capacitor during the oscillations is $1.50V$ and the maximum current through the inductor is $50.0mA$. How much time does the charge on the capacitor take to rise from zero to its maximum value?

• A. $0.238ms$
• B. $0.788ms$
• C. $0.488ms$
• D. $0.188ms$

Answer 1

The correct option is D $0.188ms$

$\frac{1}{2}L{i_0}^2=\frac{1}{2}{C{V}_0}^2$
$\therefore L=\frac{{C{V}_0}^2}{{i_0}^2}=\frac{(4\times {10}^{-6}){\left(1.5\right)}^2}{{(50\times {10}^{-3})}^2}$$=3.6\times {10}^{-3}H$

$f=\frac{1}{2\pi \sqrt{LC}}=\frac{1}{2\pi \sqrt{(3.6\times {10}^{-3})(4\times {10}^{-6})}}$
$=0.133\times {10}^{4}Hz=1.33kHz$

$t=\frac{T}{4}=\frac{1}{4f}=\frac{1}{4\times 1.33\times {10}^3}s$$=0.188\times {10}^{-3}s=0.188ms$