Question 23: AC fundamentals

Question

An ideal inductor is connected across a capacitor. Oscillations of energy $K$ are set up in the circuit. The capacitor plates are slowly drawn apart such that the frequency of oscillations is quadrupled. The work done in the process is

Accepted Answer

Resistance $R$ (ohm) has the same dimension as voltage/current. Since
Ã¢ÂÂ Voltage $V$ is work per charge: $[V]=M\,L^2\,T^{-3}\,A^{-1}$
Ã¢ÂÂ Resistance $R=V/I$
we get
$      [R]=M\,L^2\,T^{-3}\,A^{-2}.    $
Inductance $L$ (henry) follows from energy in an inductor, $E=	frac12LI^2$, so
$      [L]=\frac{E}{I^2}          =\frac{M\,L^2\,T^{-2}}{A^2}          =M\,L^2\,T^{-2}\,A^{-2}.    $
Multiply them:
$      [L\,R]      =\bigl(M\,L^2\,T^{-2}\,A^{-2}\bigr)        	imes\bigl(M\,L^2\,T^{-3}\,A^{-2}\bigr)      =M^2\,L^4\,T^{-5}\,A^{-4}.    $
That matches Option A.

Answer

15K

Answer

13K

Answer

zero

Answer

2K

AC fundamentals

An ideal inductor is connected across a capacitor. Oscillations of energy K are set up in the circuit. The capacitor plates are slowly drawn apart such that the frequency of oscillations is quadrupled. The work done in the process is

Choose the correct answer: