In a series R - C circuit, the resistance of the resistor is 4 Ω and capacitive reactance is 3 Ω. Calculate the impedance of the circuit
Question 1 Report
In a series R - C circuit, the resistance of the resistor is 4 Ω and capacitive reactance is 3 Ω. Calculate the impedance of the circuit
Answer Details
In a series R-C circuit, the total impedance (Z) is given by the square root of the sum of the squares of the resistance (R) and reactance (X). Mathematically, we can represent this as Z = sqrt(R^2 + X^2).
In this case, R = 4Ω and Xc = 3Ω. Since the capacitor has a negative reactance, we can write Xc as -1/ωC, where ω is the angular frequency of the circuit and C is the capacitance of the capacitor.
However, since we are not given the frequency or capacitance in the question, we cannot calculate the exact value of Xc. Therefore, we will assume that Xc = -3Ω, which means that the capacitive reactance cancels out part of the resistance.
Now, we can use the formula for impedance to calculate the total impedance of the circuit as follows:
Z = sqrt(R^2 + Xc^2)
Z = sqrt(4^2 + (-3)^2)
Z = sqrt(16 + 9)
Z = sqrt(25)
Z = 5Ω
Therefore, the impedance of the circuit is 5Ω.
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