Question

Calculate the potential difference across capacitor C₃?

Answer 1

The potential difference across capacitor C₃ is 15 volts.

Step-by-step explanation:

In the given circuit, capacitors C₁, C₂, and C₃ are connected in series. When capacitors are in series, the total capacitance (C_total) is given by the reciprocal of the sum of the reciprocals of individual capacitances:

`\[ \frac{1}{C_{\text{total}}} = (1)/(C_1) + (1)/(C_2) + (1)/(C_3) \]`

Let's assume the potential difference across the series combination is V. According to the definition of capacitance (Q = CV), the charge on each capacitor is given by:

`\[ Q = C_{\text{total}} \cdot V \]`

Since the capacitors are in series, the charge is the same on each capacitor. Therefore, the potential differences across the capacitors can be calculated using the individual capacitance values:

`\[ V_1 = (Q)/(C_1), \quad V_2 = (Q)/(C_2), \quad V_3 = (Q)/(C_3) \]`

Given that
`\(V_1 = 10 \, \text{V}\) and \(V_2 = 20 \, \text{V}\)`, we can use these values to find the potential difference across capacitor C₃:

`\[ V_3 = V - V_1 - V_2 \]`

Substituting the known values, we get:

`\[ V_3 = 50 \, \text{V} - 10 \, \text{V} - 20 \, \text{V} = 20 \, \text{V} \]`

Therefore, the potential difference across capacitor C₃ is 20 volts.