The total impedance of an RC circuit with a resistance of 200 Ù is 1060 Ù. If the frequency of the applied voltage is 20.0 Hz, what is the value of the capacitance in this circuit?
R^2 + Xc^2 = Z^2,
(200)^2 + Xc^2 = (1060)^2,
Xc^2 = (1060)^2 - (200)^2,
Xc^2 = 1123600 - 40000 = 1083600,
Xc = 1041 ohms.
C = 1 / (6.28*F*Xc),
C=1 / (6.28*20*1041)=7.65*10^-6 Farads.
= 7.65 Microfarads.
To find the capacitance in an RC circuit, we need to calculate the impedance value using the given resistance and total impedance values, and then use the formula for impedance in an RC circuit.
Step 1: Calculate the reactance (X) using the formula:
X = Z - R
Where:
X is the reactance
Z is the total impedance (1060 Ω)
R is the resistance (200 Ω)
X = 1060 Ω - 200 Ω
X = 860 Ω
Step 2: Calculate the capacitive reactance (Xc) using the formula:
Xc = 1 / (2πfC)
Where:
Xc is the capacitive reactance
π is a constant (approximately 3.14159)
f is the frequency (20.0 Hz)
C is the capacitance (unknown)
Rearranging the formula, we get:
C = 1 / (2πfXc)
Step 3: Substitute the values into the formula to find the capacitance:
C = 1 / (2 * 3.14159 * 20.0 Hz * 860 Ω)
C ≈ 9.26 x 10^(-6) F
Therefore, the value of the capacitance in this RC circuit is approximately 9.26 microfarads.