Question

Three capacitances 1 \(\mu\)F, 4 \(\mu\)F, and 5 \(\mu\)F are connected in parallel with a supply voltage. If the total charge flowing through the capacitors is 50 \(\mu\)C, then the supply voltage is:

• A. 2 V
• B. 10 V
• C. 6 V
• D. 3 V
• E. 5 V

Hint:

For capacitors in parallel, the total charge is the sum of the individual charges, and the voltage across each capacitor is the same.

Answer 1

Answer: (E)

For capacitors connected in parallel, the total charge \( Q \) is the sum of the charges on each capacitor: \[ Q = Q_1 + Q_2 + Q_3 \] where \( Q_1, Q_2, \) and \( Q_3 \) are the charges on each capacitor. 
The charge on each capacitor is related to the voltage across it by the formula: \[ Q = C \times V \] where \( C \) is the capacitance and \( V \) is the supply voltage.
Let the supply voltage be \( V \). Then, for each capacitor: \[ Q_1 = 1 \, \mu{F} \times V \] \[ Q_2 = 4 \, \mu{F} \times V \] \[ Q_3 = 5 \, \mu{F} \times V \] The total charge \( Q \) is the sum of these charges: \[ Q = (1 + 4 + 5) \, \mu{F} \times V = 10 \, \mu{F} \times V \] We are given that the total charge is \( 50 \, \mu{C} \). Thus: \[ 50 \, \mu{C} = 10 \, \mu{F} \times V \] Since \( 1 \, \mu{C} = 1 \, \mu{F} \times 1 \, {V} \), we can simplify the equation: \[ 50 = 10 \times V \] \[ V = \frac{50}{10} = 5 \, {V} \] Thus, the supply voltage is 5 V.
Therefore, the correct answer is option (E), 5 V.