In a series RC (resistor–capacitor) AC circuit, what qualitative effect does increasing the resistance R have on the circuit's behavior, particularly on the phase shift between the source voltage and the current?

Introduction / Context:
This question examines qualitative behavior in a series RC AC circuit when the resistance R is increased while frequency and capacitance remain fixed. In such circuits, the capacitor's reactance and the resistor determine both the current magnitude and the phase angle between the total applied voltage and the current.

Given Data / Assumptions:

• Series RC circuit excited by a sinusoidal source of fixed frequency.
• Capacitance C is constant; only R is increased.
• Standard phasor sign convention: in a capacitive circuit, current leads voltage by angle theta.

Concept / Approach:
For a series RC, the impedance is Z = R - jXc, where Xc = 1 / (2 * pi * f * C). The phase angle of the current relative to the applied voltage is theta = arctan(-Xc / R). As R increases with Xc held constant, the ratio Xc / R gets smaller, so the magnitude of the phase angle decreases in absolute value; the circuit becomes less capacitive and more resistive in behavior.

Step-by-Step Solution:
Define Xc = 1 / (2 * pi * f * C) (fixed here).Impedance: Z = R - jXc; phase angle (voltage vs current) satisfies tan(theta) = -Xc / R.Increase R → Xc / R decreases → |theta| decreases (phase shift reduces toward 0 degrees).Current magnitude I = V / |Z| also decreases because |Z| increases with larger R.

Verification / Alternative check:
Consider two cases with the same Xc: R1 and R2 where R2 > R1. Then tan(|theta2|) = Xc / R2 < Xc / R1 = tan(|theta1|), so |theta2| < |theta1|. This confirms that increasing R reduces the phase shift magnitude.

Why Other Options Are Wrong:

• No effect: False; phase and current both change with R.
• The current will increase: False; increasing R increases |Z|, so current decreases.
• The input voltage will increase: Source voltage is independent of R in this context.

Common Pitfalls:

• Confusing capacitive phase lead (current leads) with inductive lag; in RC the current leads but the lead shrinks as R grows.
• Assuming Xc changes when R changes; Xc depends only on f and C.

Final Answer:
The phase shift will decrease.