Question

In the circuit shown, a potential difference of 60V is applied across AB. The potential difference between the points M and N is

• A. 10 V
• B. 15 V
• C. 20 V
• D. 30 V

Answer 1

Answer: (D)

Step 1: Given that

The potential difference between points A and B = $60V$

Step 2: Calculation of the potential difference between the points M and N:

From the given diagram is clear that,

Capacitor of capacitances 2C, the capacitor of capacitance C between M and N and the capacitor of capacitance 2C are in series.

Therefore the potential difference along each capacitor will be different.

Let, $V_1$ , $V_{2}and{V}_3$ be the potential differences along the capacitors of capacitances 2C, C and 2C respectively.

According to the given diagram, it is clear that,

$V=60V=V_1+V_2+V_3$

Where, $V_{2}isthepotentialdifferencebetweenMandN$ .

Now, It is clear from the diagram that all three capacitors of capacitances 2C, C and 2C are in series.

Therefore the net capacitances, of the capacitors will be;

$\frac{1}{C_{net}}=\frac{1}{2C}+\frac{1}{C}+\frac{1}{2C}$

$\frac{1}{C_{net}}=\frac{1+2+1}{2C}$

$\frac{1}{C_{net}}=\frac{4}{2C}$

$C_{net}=\frac{C}{2}$

Now, we know that in series, the charges are same.

Therefore the net charge= Charge along the capacitor C between M and N

Charge= Capacitance $\times$ potential difference

Using the above formula

$C_{net}V=C_{MN}{V}_2$

$\frac{C}{2}\times 60V=C\times V_2$

$Or,$

$C\times V_2=\frac{C}{2}\times 60$

$V_2=\frac{60}{2}$

$V_2=30V$

Thus, the potential difference between M and N will be

$30V$

Thus,

Option D) $30V$ is the correct option.