HARD
JEE Main
IMPORTANT
Earn 100

In the figure below, 20.0 V battery is connected across capacitors of capacitance C1=C6=6.00 μF and C3=C5=4.00 μF, C2=C4=2.00 μF. What are (a) the equivalent capacitance Ceq of the capacitors and (b) the charge stored by Ceq? What are (c)V1 and (d)  q1 of capacitor 1, (e) V2  and (f) q2 of capacitor 2  and (g) V3 and (h) q3 of capacitor 3?

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Important Questions on Capacitance

HARD
JEE Main
IMPORTANT

Figure represents two air-filled cylindrical capacitors connected in series across a battery with potential V=10 V. Capacitor 1 has an inner plate radius of 3.00 mm, an outer plate radius of 1.5 cm, and a length of 5.0 cm. Capacitor 2 has an inner plate radius of 2.5 mm, an outer plate radius of 1.0 cm,  and a length of 9.0 cm. The outer plate of capacitor 2 is a conducting organic membrane that can be stretched, and the capacitor can be inflated to increase the plate separation. If the outer plate radius is increased to 2.5 cm by inflation, (a) how many electrons move through point P and (b) do they move toward or away from the battery?

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EASY
JEE Main
IMPORTANT
A certain substance has a dielectric constant of 5.6 and a dielectric strength of 18 MV m-1. If it is used as the dielectric material in a parallel-plate capacitor, what minimum area should the plates of the capacitor have to obtain a capacitance of 3.9×10-2 μF and to ensure that the capacitor will be able to withstand a potential difference of 4.0 kV?
MEDIUM
JEE Main
IMPORTANT

For the arrangement of figure, given below, suppose that the battery remains connected while the dielectric slab is being introduced. Calculate (a) the capacitance, (b) the charge on the capacitor plates, (c) the electric field in the gap, and (d) the electric field in the slab, after the slab is in place.

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Assume A=115 cm2d=1.24 cmV0=85.5 Vb=0.780 cm, and k=2.61.

HARD
JEE Main
IMPORTANT

In the following figure, the capacitance are C1=1.0 μF and C2=3.0 μF and both capacitors are charged to a potential difference of V=200 V but with opposite polarity as shown. Switches S1 and S2 are now closed. (a) What is now the potential difference between points a and b?

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HARD
JEE Main
IMPORTANT

Capacitor 3 in Fig. (a) is a variable capacitor (its capacitance C3 can be varied). Figure (b) gives the electric potential V1 across capacitor 1 versus C3. The horizontal scale is set by C3s=12.0 μF. Electric potential V1 approaches an asymptote of 8.0V as C3. What are (a) the electric potential V across the battery, (b) C1,and (c) C2?

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(a)                                                                             (b)

HARD
JEE Main
IMPORTANT

The capacitors in Fig. are initially uncharged. The capacitance are C1=4.0 μF, C2=8.0 μF and C3=12 μF, and the battery's potential difference is V=6.0 V. When switch S is closed, how many electrons travel through (a) point a (b) point b,(c) point c and (d) point d ? In the figure, do the electrons travel up or down through (e) point b and (f) point c?

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MEDIUM
JEE Main
IMPORTANT

The figure shows a circuit section of four air-filled capacitors that is connected to a larger circuit. The graph below the section shows the electric potential V(x) as a function of position x along the lower part of the section, through capacitor 4. Similarly, the graph above the section shows the electric potential V(x) as a function of position x along the upper part of the section, through capacitors 1,2, and 3. Capacitor 3 has a capacitance of 1.60 μF. What are the capacitance of (a) capacitor 1 and (b) capacitor 2 ?

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MEDIUM
JEE Main
IMPORTANT

A charged isolated metal sphere of diameter15 cm has a potential of 6500 V relative to V=0 at infinity.

(a) Calculate the energy density in the electric field near the surface of the sphere.

(b) If the diameter is decreased, does the energy density near the surface increase, decrease or remain the same?