A (25/pie square) microF Capacitor `C` and a 50 ohm resistor `R` are connected in series to a 220V, 50Hz a.c. supply. It`s is desired to have a current of 2A in phase with supply voltage.Find the value(s) of additional component(s) to be connected in series with `C` and `R`

To achieve a current of 2A in phase with the supply voltage in a circuit consisting of a capacitor and a resistor connected in series, we need to analyze the impedance of the circuit and determine what additional components may be required. Let's break this down step by step.

Understanding the Circuit Components

We have the following components in our circuit:

• Capacitance (C): 25/pie square microfarads (µF)
• Resistance (R): 50 ohms
• Supply Voltage (V): 220V
• Frequency (f): 50Hz

Calculating Capacitive Reactance

The capacitive reactance (X_C) can be calculated using the formula:

X_C = 1 / (2 * π * f * C)

First, we need to convert the capacitance from microfarads to farads:

C = 25/pie square µF = 25 / (π² * 10^-6) F

Now substituting the values:

X_C = 1 / (2 * π * 50 * (25 / (π² * 10^-6)))

X_C = 1 / (2 * 50 * 25 / (π * 10^-6)) = π * 10^-6 / 2500

X_C ≈ 1.2566 * 10^-3 ohms

Calculating Total Impedance

The total impedance (Z) of the series circuit is given by:

Z = √(R² + X_C²)

Substituting the values:

Z = √(50² + (1.2566 * 10^-3)²)

Z ≈ √(2500 + 0.00000158) ≈ 50 ohms

Finding the Required Current

Using Ohm's law (V = I * Z), we can find the current:

I = V / Z = 220V / 50 ohms = 4.4A

However, we want the current to be 2A. This means we need to adjust the impedance to achieve this current level.

Adjusting Impedance with Additional Components

To reduce the current to 2A while maintaining the same voltage, we need to increase the total impedance. The required impedance (Z_required) can be calculated as:

Z_required = V / I = 220V / 2A = 110 ohms

Calculating Additional Resistance Needed

Since we already have a resistance of 50 ohms, we need an additional resistance (R_add) to achieve the total impedance:

Z_required = R + R_add → 110 = 50 + R_add

R_add = 110 - 50 = 60 ohms

Conclusion

To achieve a current of 2A in phase with the supply voltage, you need to connect an additional resistor of 60 ohms in series with the existing 50-ohm resistor and the capacitor. This will ensure that the total impedance of the circuit is 110 ohms, allowing the desired current to flow.