Question

A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be

A. $$\frac{1}{2}$$  
B. $$1$$
C. $$2$$
D. $$\frac{1}{4}$$
Answer :   $$\frac{1}{2}$$
Solution :
Required ratio
$$ = \frac{{{\text{Energy stored in capacitor}}}}{{{\text{Workdone by the battery}}}} = \frac{{\frac{1}{2}C{V^2}}}{{C{e^2}}}$$
where $$C =$$  Capacitance of capacitor
$$V =$$  Potential difference,
$$e =$$  emf of battery
$$\frac{{\frac{1}{2}C{e^2}}}{{C{e^2}}} = \frac{1}{2}\,\,\,\,\,\,\,\,\left( {\because V = e} \right)$$

Releted MCQ Question on
Electrostatics and Magnetism >> Electric Current

Releted Question 1

The temperature coefficient of resistance of a wire is 0.00125 per $$^ \circ C$$ At $$300\,K,$$  its resistance is $$1\,ohm.$$  This resistance of the wire will be $$2\,ohm$$  at.

A. $$1154\,K$$
B. $$1100\,K$$
C. $$1400\,K$$
D. $$1127\,K$$
Releted Question 2

A constant voltage is applied between the two ends of a uniform metallic wire. Some heat is developed in it. The heat developed is doubled if

A. both the length and the radius of the wire are halved.
B. both the length and the radius of the wire are doubled.
C. the radius of the wire is doubled.
D. the length of the wire is doubled.
Releted Question 3

The electrostatic field due to a point charge depends on the distance $$r$$ as $$\frac{1}{{{r^2}}}.$$ Indicate which of the following quantities shows same dependence on $$r.$$

A. Intensity of light from a point source.
B. Electrostatic potential due to a point charge.
C. Electrostatic potential at a distance r from the centre of a charged metallic sphere. Given $$r$$ < radius of the sphere.
D. None of these
Releted Question 4

The current $$i$$ in the circuit (see Fig) is
Electric Current mcq question image

A. $$\frac{1}{{45}}A$$
B. $$\frac{1}{{15}}A$$
C. $$\frac{1}{{10}}A$$
D. $$\frac{1}{5}A$$

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Electric Current


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