Effect of Resistance on Current and Power Factor in R-C Series Circuit

**Introduction:**
In an R-C series circuit, a resistor (R) and a capacitor (C) are connected in series with each other. The circuit is typically driven by an AC voltage source. The resistor and capacitor have different effects on the current and power factor of the circuit. When the resistance of the R-C series circuit increases, it has the following effects:

**1. Effect on Current:**
- The current in an R-C series circuit is given by the equation: I = V/Z, where I is the current, V is the voltage, and Z is the impedance of the circuit.
- The impedance of the circuit is given by: Z = √(R^2 + (1/ωC)^2), where R is the resistance, ω is the angular frequency, and C is the capacitance.
- As the resistance (R) increases, the impedance (Z) of the circuit also increases. This leads to a decrease in the current (I) flowing through the circuit.
- This is because the increase in resistance restricts the flow of current, resulting in a decrease in the overall current in the circuit.

**2. Effect on Power Factor:**
- Power factor is a measure of how effectively an AC circuit converts electrical power into useful work. It is defined as the cosine of the angle between the voltage and current waveforms.
- The power factor (PF) of an R-C series circuit is given by: PF = cos(θ), where θ is the phase angle between the current and the voltage.
- The phase angle (θ) is given by: θ = arctan((1/ωCR)), where R is the resistance, C is the capacitance, and ω is the angular frequency.
- As the resistance (R) increases, the phase angle (θ) also increases. This leads to a decrease in the power factor (PF) of the circuit.
- A higher phase angle indicates a greater phase difference between the current and voltage waveforms, resulting in a lower power factor.
- A lower power factor means that the circuit is less efficient in converting electrical power into useful work.

**Conclusion:**
When the resistance of an R-C series circuit increases, the current flowing through the circuit decreases, and the power factor of the circuit decreases as well. These effects are due to the increase in impedance and phase angle caused by the higher resistance. It is important to consider these effects when designing and analyzing R-C series circuits to ensure efficient and effective operation.

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