An A.c circuit consist of 3uf capacitor and 500ohm resistor in series. If the current voltage applied is 12v and and frequency 50Hz. Calculate 1. Current though the circuit 2. Voltage accross the capacitor 3 phase angle 4 average power supplied 5 power factor

See previous post.

To calculate the values in the given AC circuit, we can follow these steps:

1. Current through the circuit (I):
The current in an AC circuit can be found using the Ohm's Law formula for AC circuits:
I = V / Z
where I is the current, V is the voltage, and Z is the impedance of the circuit.

In this case, the impedance is given by the series combination of the resistor and capacitor, which can be calculated as:
Z = √(R^2 + (1 / (ωC))^2)
where R is the resistor value, C is the capacitor value, and ω is the angular frequency (2πf, where f is the frequency in Hz).

Substituting the given values:
R = 500 ohms
C = 3 μF = 3 × 10^(-6) F
f = 50 Hz

ω = 2πf = 2π * 50 = 314.16 rad/s

Now, plug these values into the impedance equation:
Z = √(500^2 + (1 / (314.16 * 3 × 10^(-6)))^2) ≈ 500.532 ohms

Finally, use Ohm's Law:
I = V / Z = 12V / 500.532Ω ≈ 0.024 A

Therefore, the current through the circuit is approximately 0.024 Amperes.

2. Voltage across the capacitor (VC):
The voltage across the capacitor can be found using the relationship between current and voltage in a capacitor in an AC circuit:
VC = I / (jωC)
where VC is the voltage across the capacitor, I is the current, ω is the angular frequency, and C is the capacitor value.

Using the values we have:
I = 0.024 A
ω = 314.16 rad/s
C = 3 × 10^(-6) F

Substituting these values:
VC = 0.024 A / (j * 314.16 rad/s * 3 × 10^(-6)) = (0.024 A / j) * (1 / (314.16 rad/s * 3 × 10^(-6))) ≈ 25.52 V

So, the voltage across the capacitor is approximately 25.52 Volts.

3. Phase angle (θ):
The phase angle tells us the phase relationship between the voltage and current waveforms in an AC circuit. In this case, it can be calculated using the formula:
θ = atan((-1 / (ωC * R)))

Using the given values:
ω = 314.16 rad/s
C = 3 × 10^(-6) F
R = 500 ohms

Substituting these values:
θ = atan((-1 / (314.16 rad/s * 3 × 10^(-6) * 500))) ≈ -0.058 radians ≈ -3.33 degrees

Therefore, the phase angle is approximately -3.33 degrees.

4. Average power supplied:
The average power in an AC circuit can be calculated using the formula:
Pavg = VI * cos(θ)
where Pavg is the average power, V is the voltage, I is the current, and θ is the phase angle.

Using the given values:
V = 12V
I = 0.024 A
θ = -3.33 degrees ≈ -0.058 radians

Substituting these values:
Pavg = 12V * 0.024 A * cos(-0.058 radians) ≈ 0.286 W

The average power supplied is approximately 0.286 Watts.

5. Power factor:
The power factor is the ratio of the real power to the apparent power in an AC circuit and can be calculated using the formula:
Power factor (PF) = cos(θ)

Using the given phase angle:
θ = -3.33 degrees ≈ -0.058 radians

The power factor is given by:
PF = cos(-0.058 radians) ≈ 0.998

Therefore, the power factor is approximately 0.998.