Name: Force Between Capacitor Plates
Uploaded: 2019-07-19
Duration: 2 min 26 s
Description: In this video, let us derive the expression for the electrostatic force acting between the parallel plates of a capacitor. Watch this video to learn.

Question

In figure, the system is in steady state. Then

(a) $V_{A} - V_{B} =$ _____

(b) $V_{B} - V_{C} =$ _____

(c) $V_{D} - V_{E} =$ _____

(d) The energy stored in the circuit is ______

Accepted Answer

Both $3 μF$ capacitors will be in parallel, and similarly upper two $1 μF$ capacitors will be in parallel. The circuit may be redrawn as follows.

Equivalent of two parallel capacitors between $A$ and $B$ is given as $C_{AB} = 3 + 3 = 6 μF$
Equivalent of two parallel capacitors between $B$ and $C$ is given as $C_{BC} = 1 + 1 = 2 μF$

Now the equivalent circuit will look like as shown below.

Equivalent of series resistors in branch $A C$ is given as $C_{AC} = \frac{6 \times 2}{6 + 2} = \frac{3}{2} μF$ .
Since, branch $A C$ and $D E$ are parallel to battery. Charge in branch $A C$ is given as $q_{1} = 100 (\frac{3}{2}) = 150 μC$ . Similarly, charge in branch $D E$ is given as $q_{2} = 100 (1) = 100 μC$

Now charge on $6 μF$ and $2 μF$ is $150 μC$ and charge on $1 μF$ is $100 μC$ .

Potential difference between $A$ and $B$ is $V_{A} - V_{B} = \frac{q_{1}}{6} = \frac{150}{6} = 25 V$

Potential difference between $A$ and $C$ is $V_{A} - V_{C} = \frac{q_{1}}{(\frac{3}{2})} = \frac{150}{(\frac{3}{2})} = 75 V$

Potential difference between $D$ and $E$ is $V_{D} - V_{E} = \frac{q_{2}}{1} = \frac{100}{1} = 100 V$

Equivalent capacitance of the circuit is given as $C_{eq} = C_{AC} + C_{DE} = \frac{3}{2} + 1 = \frac{5}{2} μF$ .

Energy stored in the capacitor is given as $U = \frac{1}{2} C_{eq} V^{2} = \frac{1}{2} (\frac{5}{2} \times 10^{- 6}) \times {(100)}^{2}$
$\Rightarrow U = 125 \times 10^{- 4} J = 12.5 mJ$

In figure, the system is in steady state. Then

(a) $V_{A} - V_{B} =$ _____

(b) $V_{B} - V_{C} =$ _____

(c) $V_{D} - V_{E} =$ _

(d) The energy stored in the circuit is __

Important Questions on Capacitor and Capacitance

Learn and Prepare for any exam you want !

In figure, the system is in steady state. Then (a) VA-VB=_____ (b) VB-VC=_____ (c) VD-VE=_____ (d) The energy stored in the circuit is ______

Important Questions on Capacitor and Capacitance

Learn and Prepare for any exam you want !

In figure, the system is in steady state. Then

(a) $V_{A} - V_{B} =$ _____

(b) $V_{B} - V_{C} =$ _____

(c) $V_{D} - V_{E} =$ _

(d) The energy stored in the circuit is __