Two 4F capacitors are connected in series, calculate the voltage across each if the total voltage is 20V.
A
$10\ V$
B
$5\ V$
C
$20\ V$
D
$0\ V$

Question

Two 4F capacitors are connected in series, calculate the voltage across each if the total voltage is 20V.

Examoogle · Accepted Answer

$10\ V$

Explanation: Given: Capacitance C1 = 4F, Capacitance C2 = 4F, Total voltage V = 20V. The capacitors are in series.

Formula Used: $$V_x = V 	imes \frac{C_{eq}}{C_x}$$ or simply $$V_1 = V_2 = \frac{V}{n}$$

Steps: Identify the circuit configuration: Since the two capacitors are identical ($C_1 = C_2 = 4F$) and connected in series, the total voltage $V$ will be distributed equally across them.. Apply voltage distribution principle: In a series circuit with equal capacitors, the voltage drops are identical: $V_1 = V_2$. Since the total voltage is $V = 20V$, we divide by the number of capacitors $n=2$.. Calculate the final voltage: Performing the division gives the voltage across each capacitor.

Answer: A is correct because when two identical capacitors are connected in series, the total voltage is divided equally across them, resulting in $10V$ for each.

Exam Tip: This concept is the inverse of resistors in series; remember that for capacitors in series, the voltage divides according to the reciprocal of capacitance, whereas resistors divide according to their individual resistance values.

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