The equivalent capacitance of the circuit shown below is
A) 0.2 C.
B) 0.4 C.
C) 1 C.
D) 4 C.
E) 5 C.

Question

The equivalent capacitance of the circuit shown below is 
A) 0.2 C. 
B) 0.4 C. 
C) 1 C. 
D) 4 C. 
E) 5 C.

Quizplus · Accepted Answer

The circuit consists of two parallel combinations of resistors and capacitors. The equivalent capacitance of the bottom combination (C4 and C5) is C4 + C5 = 2 + 2 = 4. The equivalent capacitance of the top combination (C2, C3, and the parallel combination of C1 and the series combination of C6 and C7) can be found by using the formula for capacitors in parallel and capacitors in series. The parallel combination of C1 and the series combination of C6 and C7 is equivalent to C6 + C7 = 3. The equivalent capacitance of the top combination is then C2 + C3 + (C6 + C7)⁻¹ = 1 + 2 + (3)⁻¹ = 2 + ⅓ = 6/3 + 1/3 = 7/3.The equivalent capacitance of the circuit is the sum of the equivalent capacitance of the two combinations, or 4 + 7/3 = 19/3. This is approximately equal to 6.3. The correct answer is therefore D, 4 C.

The Equivalent Capacitance of the Circuit Shown Below Is