State effect on value of impedance, current and power factor of circuit when resistance of R-C series circuit increases?

**Effect of increasing resistance on impedance, current, and power factor in an R-C series circuit**

In an R-C series circuit, the impedance, current, and power factor are influenced by the resistance value. Let's discuss in detail how these parameters are affected when the resistance of the circuit increases.

**1. Impedance:**
Impedance is the total opposition offered to the flow of alternating current in a circuit. It consists of resistance (R) and reactance (X). In an R-C series circuit, the reactance is provided by the capacitor (Xc = 1/(2πfC)), where f is the frequency and C is the capacitance.

When the resistance value increases in the circuit, the impedance also increases. This is because impedance is directly proportional to resistance. The formula for impedance in an R-C series circuit is Z = √(R^2 + Xc^2). As R increases, the total impedance value increases.

**2. Current:**
The current flowing through an R-C series circuit is given by the formula I = V/Z, where V is the applied voltage and Z is the impedance.

When the resistance value increases, the current flowing through the circuit decreases. This is because the increase in resistance results in a higher impedance value. As per Ohm's Law (V = I * R), a higher resistance for the same applied voltage will lead to a lower current. Therefore, an increase in resistance reduces the current in the circuit.

**3. Power Factor:**
Power factor is a measure of how effectively the circuit uses the available electrical power. It is the cosine of the phase angle between the voltage and current waveforms.

When the resistance value increases in an R-C series circuit, the power factor decreases. This is because the power factor is given by the formula PF = cos(θ), where θ is the phase angle between voltage and current.

In an R-C series circuit, the current lags behind the voltage due to the presence of the reactive component (capacitance). When the resistance increases, the effect of the reactive component becomes relatively smaller, and the phase angle decreases. As a result, the power factor decreases.

**Conclusion:**
Increasing the resistance in an R-C series circuit leads to an increase in impedance, a decrease in current, and a decrease in power factor. These changes occur due to the direct relationship between resistance and impedance, the inverse relationship between resistance and current, and the decrease in phase angle caused by the increase in resistance.