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1.

What will be the effect on the potential between the plates of a charged parallel plate capacitor when both plates are carry nearest to each other. While the charge is constant. Explain?

Answer»

q = CV
⇒ V = \(\frac{q}{C}\)
or, V ∝ \(\frac{1}{C}\) (when charge is constant)
On bringing them near d decreases but according to C = \(\frac{\varepsilon_{0} A}{d}\), C increases. Due to which potential d difference between plates decreases.

2.

The potential energy between plates of a charged parallel plate capacitor is UQ. If a dielectric plate of dielectric constant er is placed between The gap of plates, then the new potential energy will be :(a) \(\frac{U_{0}}{\varepsilon_{r}}\)(b) U0εr2(c) \(\frac{U_{0}}{\varepsilon_{r}^{2}}\)(d) U0

Answer»

(a) \(\frac{U_{0}}{\varepsilon_{r}}\)
Energy decreases to εr times
U = \(\frac{U_{0}}{\varepsilon_{r}}\)

3.

What is the resultant electric field between the plates of a charged parallel plate capacitor when the surface charge density of plates is σ?

Answer»

Resultant electric field E = \(\frac{\sigma}{\varepsilon_{0}}\)

4.

On what factors does the capacitance of a conductor depend?

Answer»

The capacitance of a conductor depend on area of cross-section and medium surrounding the conductor.

5.

Eight Mercury drops of equal radius and equal charge combine to form a big drop. The capacitance of big drop in comparison the each small drop will be:(a) 2 times(b) 8 times(c) 4 times(d) 16 times

Answer»

(a) 2 times
Volume of big drop = 8 × Volume of small drop
\(\frac{4}{3}\)πR3 = 8 × \(\frac{4}{3}\)πr3
R = 2r
Capacitance of small drop C1 = 4πε0r
Capacitance of bigger drop C2 = 4πε0R
\(\frac{C_{1}}{C_{2}}=\frac{r}{R}=\frac{r}{2 r}\)
C2 = 2C2