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

Xc = 1/W*C = 1/314.2*3*10^-6 = 1061 Ohms

Z = R-jXc = 500 -j1061 = 1173[-64.8o].

1. I = V/Z=12/1173[-64.8o]=0.01023[64.8]

2. Vc= I * Xc = 0.01023[64.8]*1061[-90o]= 10.85 Amps.[-25.2o]

3. A = -25.2o

4. P = I^2*R = (0.01023)^2 * 500= 0.0523 W.

5. Pf = cosA = cos(-64.8) = 0.426

To calculate various parameters of the AC circuit, we can use the following formulas:

1. Calculate the current through the circuit (I) using Ohm's law:
I = Voltage / Resistance

2. Calculate the voltage across the capacitor (Vc) using the impedance of the capacitor (Zc) formula:
Zc = 1 / (2πfC) where f is the frequency in Hz, and C is the capacitance in farads.
Vc = I * Zc

3. Calculate the phase angle (θ) between the current and the voltage using the formula:
θ = arctan(Zc / R)

4. Calculate the average power supplied using the formula:
Average Power = Voltage * Current * Cos(θ)

5. Calculate the power factor using the formula:
Power Factor = Cos(θ)

Given:
Voltage (V) = 12V
Frequency (f) = 50Hz
Capacitance (C) = 3μF = 3 * 10^(-6) F
Resistance (R) = 500Ω

Let's calculate the parameters step by step:

1. Current through the circuit (I):
I = V / R
I = 12V / 500Ω
I ≈ 0.024A

2. Voltage across the capacitor (Vc):
Zc = 1 / (2πfC)
Zc = 1 / (2 * 3.14 * 50Hz * 3 * 10^(-6)F)
Zc ≈ 1062.65Ω
Vc = I * Zc
Vc ≈ 0.024A * 1062.65Ω
Vc ≈ 25.50V

3. Phase angle (θ):
θ = arctan(Zc / R)
θ = arctan(1062.65Ω / 500Ω)
θ ≈ 1.105 radians

4. Average power supplied:
Average Power = V * I * Cos(θ)
Average Power = 12V * 0.024A * Cos(1.105 radians)
Average Power ≈ 0.278W

5. Power factor:
Power Factor = Cos(θ)
Power Factor ≈ Cos(1.105 radians)
Power Factor ≈ 0.478

So, the calculated values for the given AC circuit are:
1. Current through the circuit ≈ 0.024A
2. Voltage across the capacitor ≈ 25.50V
3. Phase angle ≈ 1.105 radians
4. Average power supplied ≈ 0.278W
5. Power factor ≈ 0.478

To calculate the various parameters of the AC circuit, we can use the formulas and concepts of AC circuit analysis. Let's calculate each parameter step by step:

1. Current through the circuit (I):
In an AC circuit with a capacitor and a resistor in series, the total current is given by the formula:
I = V / Z
where V is the voltage applied and Z is the impedance of the circuit.

To calculate impedance, we need to calculate the reactance of the capacitor and resistance:
Reactance of the capacitor (Xc):
Xc = 1 / (2 * π * f * C)
where f is the frequency and C is the capacitance.

Impedance (Z):
Z = √(R^2 + Xc^2)
where R is the resistance.

Now, we can substitute the given values and calculate the current:
Xc = 1 / (2 * π * 50 * 3e-6) = 1062.03 Ω (approximately)
Z = √(500^2 + 1062.03^2) = 1192.1 Ω (approximately)
I = 12 V / 1192.1 Ω ≈ 0.0101 A

Therefore, the current through the circuit is approximately 0.0101 A.

2. Voltage across the capacitor (Vc):
In a series circuit, the voltage across each component is the same as the total circuit voltage.
Therefore, the voltage across the capacitor is 12 V.

3. Phase angle (φ):
The phase angle can be measured by finding the ratio of the reactive component (Xc) to the total impedance (Z) and taking the arctangent.
φ = arctan(Xc / R)

Substituting the values:
φ = arctan(1062.03 Ω / 500 Ω) ≈ 64.22 degrees

Therefore, the phase angle is approximately 64.22 degrees.

4. Average power supplied:
The average power supplied to the circuit can be calculated as P = I * V * cos(φ), where I is the current, V is the voltage, and φ is the phase angle.

Substituting the values:
P = 0.0101 A * 12 V * cos(64.22 degrees) ≈ 0.248 W

Therefore, the average power supplied to the circuit is approximately 0.248 W.

5. Power factor:
The power factor is the ratio of the real power (P) to the apparent power (S), which is the product of current and voltage: S = I * V.
Power factor = P / S

Substituting the values:
S = 0.0101 A * 12 V ≈ 0.1212 VA
Power factor = 0.248 W / 0.1212 VA ≈ 2.04

Therefore, the power factor is approximately 2.04.