An RC circuit with resistance R₀ and capacitance C₀ has a time constant τ₀.Which of the following additions to the circuit would result in the time constant doubling? A)a capacitor with capacitance 3C₀in series with the original C₀ B)a capacitor with capacitance C₀ in series with the original C₀ C)a capacitor with capacitance 3C₀ in parallel with the original C₀ D)a capacitor with capacitance C₀ in parallel with the original C₀

Question

Quizplus · Accepted Answer

The formula for the time constant of an RC circuit is τ = RC. Doubling this time constant would mean doubling the product RC. 
For options A and B, adding a capacitor in series with the original capacitor would reduce the equivalent capacitance of the circuit, thereby increasing the time constant (τ = R(C+C/2) = RC + 0.5RC = 1.5RC). This would not result in a doubling of the time constant. 
For options C and D, adding a capacitor in parallel with the original capacitor would increase the equivalent capacitance of the circuit, thereby decreasing the time constant (τ = R(C+3C)/3 = RC, where R and C are the same as before). This would result in a doubling of the time constant. 
Therefore, the correct choice is D, adding a capacitor with capacitance C in parallel with the original capacitor.

An RC Circuit with Resistance R​0 and Capacitance C​0 Has

An RC Circuit with Resistance R₀ and Capacitance C₀ Has