Question

Two thin dielectric slabs of dielectric constants $${K_1}$$ and $${K_2}\left( {{K_1} < {K_2}} \right)$$   are inserted between plates of a parallel plate capacitor, as shown in the figure.
Capacitors and Dielectrics mcq question image
The variation of electric field $$E$$ between the plates with distance $$d$$ as measured from plate $$P$$ is correctly shown by

A. Capacitors and Dielectrics mcq option image
B. Capacitors and Dielectrics mcq option image
C. Capacitors and Dielectrics mcq option image  
D. Capacitors and Dielectrics mcq option image
Answer :   Capacitors and Dielectrics mcq option image
Solution :
Graph (C) will be the right graph, the electric field inside the dielectrics will be less than the electric field outside the dielectrics. The electric field inside the dielectrics could not be zero.
Capacitors and Dielectrics mcq solution image
As $${K_2} > {K_1},$$   the drop in electric field for $${K_2}$$ dielectric must be more than $${K_1}.$$

Releted MCQ Question on
Electrostatics and Magnetism >> Capacitors and Dielectrics

Releted Question 1

A parallel plate capacitor of capacitance $$C$$ is connected to a battery and is charged to a potential difference $$V.$$ Another capacitor of capacitance $$2C$$ is similarly charged to a potential difference $$2V.$$ The charging battery is now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is

A. zero
B. $$\frac{3}{2}C{V^2}$$
C. $$\frac{{25}}{6}C{V^2}$$
D. $$\frac{9}{2}C{V^2}$$
Releted Question 2

Two identical metal plates are given positive charges $${Q_1}$$ and $${Q_2}\left( { < {Q_1}} \right)$$   respectively. If they are now brought close together to form a parallel plate capacitor with capacitance $$C,$$ the potential difference between them is

A. $$\frac{{\left( {{Q_1} + {Q_2}} \right)}}{{2C}}$$
B. $$\frac{{\left( {{Q_1} + {Q_2}} \right)}}{C}$$
C. $$\frac{{\left( {{Q_1} - {Q_2}} \right)}}{C}$$
D. $$\frac{{\left( {{Q_1} - {Q_2}} \right)}}{{2C}}$$
Releted Question 3

For the circuit shown in Figure, which of the following statements is true?
Capacitors and Dielectrics mcq question image

A. With $${S_1}$$ closed $${V_1} = 15\,V,{V_2} = 20\,V$$
B. With $${S_3}$$ closed $${V_1} = {V_2} = 25\,V$$
C. With $${S_1}$$ and $${S_2}$$ closed, $${V_1} = {V_2} = 0$$
D. With $${S_1}$$ and $${S_3}$$ closed, $${V_1} = 30\,V,{V_2} = 20\,V$$
Releted Question 4

A parallel plate capacitor of area $$A,$$ plate separation $$d$$ and capacitance $$C$$ is filled with three different dielectric materials having dielectric constants $${k_1},{k_2}$$  and $${k_3}$$ as shown. If a single dielectric material is to be used to have the same capacitance $$C$$ in this capacitor, then its dielectric constant $$k$$ is given by
Capacitors and Dielectrics mcq question image

A. $$\frac{1}{K} = \frac{1}{{{K_1}}} + \frac{1}{{{K_2}}} + \frac{1}{{2{K_3}}}$$
B. $$\frac{1}{K} = \frac{1}{{{K_1} + {K_2}}} + \frac{1}{{2{K_3}}}$$
C. $$K = \frac{{{K_1}{K_2}}}{{{K_1} + {K_2}}} + 2{K_3}$$
D. $$K = {K_1} + {K_2} + 2{K_3}$$

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