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

The figure shows a network of seven capacitors. If charge on $5 μF$ capacitor is $10 μC$ , find the potential difference between points $A$ and $C$.

Accepted Answer

The given circuit is,

Given,

Charge in $5 μF$ capacitor is $10 μC$ .
That is, the potential difference across $5 μF$ capacitor is:
$V_{AD} = \frac{q}{C} = \frac{10 \times 10^{- 6}}{5 \times 10^{- 6}} = 2 V$ .

Since $3 μF$ , $4 μF$ and $5 μF$ capacitors are connected in parallel across the points $A$ and $D$ ,

The voltage across each of them will be same, and it is $V_{AD} = 2 V$ .

The charge in $3 μF$ capacitor $= C V_{AD} = 3 \times 10^{- 6} \times 2 = 6 μC$ and
The charge in $4 μF$ capacitor $= 4 \times 10^{- 6} \times 2 = 8 μC$ .

Now, the total charge flowing in upper branch of the circuit is:
$q_{upper} = 10 μC + 6 μC + 8 μC$

$\Rightarrow q_{upper} = 24 μC$ .
Potential difference across $C_{2}$ is $\frac{q_{upper}}{C_{1}}$

$\Rightarrow \frac{24 μC}{4 μC} = 6 V$ .
Total potential difference across $A B$ is

$V_{AB} = 6 + 2 = 8 V$ .

In the lower branch, the parallel combination of $4 μF$ and $2 μF$ is in series with $3 μF$ .

Thus, the equivalent capacitance of lower branch of the circuit is
$\Rightarrow \frac{(4 + 2) \times 3}{(4 + 2) + 3} = 2 μC$ .
The net charge through the lower branch of the circuit $= (2 \times 10^{- 6}) (8) = 16 μC$ .

Hence, the charge in capacitor $C_{1} = 3 μF$ is $16 μC$ .
Therefore, the potential difference between $A$ and $C$ is
$V_{AC} = \frac{q_{lower}}{C_{1}} = \frac{16 μC}{3 μF}$ ,

$∴ V_{AC} = 5 .33 V$ .

The figure shows a network of seven capacitors. If charge on $5 μF$ capacitor is $10 μC$ , find the potential difference between points $A$ and $C$.

Important Questions on Capacitor and Capacitance

Learn and Prepare for any exam you want !

The figure shows a network of seven capacitors. If charge on 5 μF capacitor is 10 μC, find the potential difference between points $A$ and $C$.

Important Questions on Capacitor and Capacitance

Learn and Prepare for any exam you want !

The figure shows a network of seven capacitors. If charge on $5 μF$ capacitor is $10 μC$ , find the potential difference between points $A$ and $C$.