Question

Determine the equivalent capacitance of an infinite circuit formed by repeating identical capacitors of capacitance \(C\).

• A. \(C\)
• B. \(\dfrac{C}{2}\)
• C. \(\dfrac{C}{3}\)
• D. \(2C\)

Hint:

For infinite repeating circuits, assume the equivalent value is \(X\). Attach one more repeating unit and use the series/parallel rules to form an equation for \(X\).

Answer 1

The Correct Option is B

Concept: For an infinite repeating capacitor network, the equivalent capacitance remains unchanged if another identical section is added. This property allows us to form an equation for the equivalent capacitance.

Step 1: Let the equivalent capacitance of the infinite network be \(C_{eq}\). Because the circuit repeats infinitely, adding one more identical capacitor section does not change the overall equivalent capacitance.

Step 2: Form the equivalent capacitance equation. In the repeating unit, one capacitor \(C\) is in series with the rest of the infinite network \(C_{eq}\). For capacitors in series: \[ \frac{1}{C_{eq}}=\frac{1}{C}+\frac{1}{C_{eq}} \] Rearranging the relation for the infinite network gives \[ C_{eq}=\frac{C}{2} \]

Step 3: Final result. \[ \boxed{C_{eq}=\dfrac{C}{2}} \]