A circuit consist of a capacitor of 10^-4F and a resistor of 100 ohms an alternating emf of 20Vrms and frequency of 50/π H is applied determine
The peak current flowing
The voltage across the capacitor
The average power supplied
To determine the peak current flowing in the circuit, we can use Ohm's Law. The formula to calculate peak current is:
I_peak = V_peak / R
Where V_peak is the peak voltage and R is the resistance.
Since the given voltage is in RMS (Root Mean Square), we need to convert it to peak voltage by multiplying it by the square root of 2:
V_peak = V_rms * √2
V_rms = 20V (given)
V_peak = 20V * √2
= 20V * 1.414
≈ 28.28V
Now, we can calculate the peak current as follows:
I_peak = V_peak / R
= 28.28V / 100Ω
= 0.2828A
The peak current flowing through the circuit is approximately 0.2828A.
To determine the voltage across the capacitor, we can use the formula for the impedance of a capacitor in an AC circuit:
Z_c = 1 / (2πfC)
Where Z_c is the impedance of the capacitor, f is the frequency, and C is the capacitance.
Given:
C = 10^-4F
f = 50/π
Substituting the values:
Z_c = 1 / (2π * (50/π) * 10^-4)
= 1 / (2 * 50 * 10^-4)
= 1 / (100 * 10^-4)
= 1 / 10^-2
= 100Ω
Since the impedance of the capacitor is equal to the resistance, the voltage across the capacitor will be equal to the RMS voltage, which is 20V.
The voltage across the capacitor is 20V.
To determine the average power supplied to the circuit, we can use the formula:
P_avg = (V_rms^2) / R
Substituting the values:
P_avg = (20V)^2 / 100Ω
= 400V^2 / 100Ω
= 400W / 100Ω
= 4W
The average power supplied to the circuit is 4W.
To determine the peak current flowing in the circuit, we can use the formula for the current in an AC circuit:
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 can be calculated using the formula:
Z = √(R^2 + (1 / (ωC))^2)
Where R is the resistance, ω is the angular frequency (2πf), and C is the capacitance.
Given:
R = 100 ohms
C = 10^-4 F
Vrms = 20V
f = 50/π Hz
First, calculate the angular frequency:
ω = 2πf
= 2π * (50/π)
= 100π
Next, calculate the impedance:
Z = √(R^2 + (1 / (ωC))^2)
= √((100^2) + (1 / ((100π)(10^-4)))^2)
Now, we can calculate the peak current using the formula:
I = V / Z
= (20) / Z
To determine the voltage across the capacitor, we can use the formula:
VC = VR
Given that VC is the voltage across the capacitor and VR is the voltage across the resistor, we know that VR is equal to Vrms.
VC = Vrms = 20V
Finally, to determine the average power supplied, we can use the formula:
P = I^2 * R
Where P is the power, I is the current, and R is the resistance.
P = (I^2) * R
Now you can substitute the value of I obtained earlier and the given value of R to calculate the average power supplied.