In a series R-L-C circuit, R = 10\(\Omega\), \(X_{c}\)= 4\(\Omega\) and \(X_{L}\) = 9\(\Omega\). The impedance of the circuit is
Question 1 Report
In a series R-L-C circuit, R = 10\(\Omega\), \(X_{c}\)= 4\(\Omega\) and \(X_{L}\) = 9\(\Omega\). The impedance of the circuit is
Answer Details
The impedance of a circuit is the total opposition to the flow of an alternating current, consisting of both resistance and reactance. The formula for impedance in a series R-L-C circuit is:
Z = \(\sqrt{R^2 + (X_L - X_C)^2}\)
where R is the resistance, \(X_L\) is the inductive reactance, and \(X_C\) is the capacitive reactance.
Substituting the given values, we get:
Z = \(\sqrt{10^2 + (9 - 4)^2}\) = \(\sqrt{100 + 25}\) = \(\sqrt{125}\) = 11.2\(\Omega\)
Therefore, the impedance of the given series R-L-C circuit is 11.2\(\Omega\).
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