The RLC series circuit shown in Figure 24–8 contains an inductor with an inductive reactance of 62 Ω and a capacitor with a capacitive reactance of 38 Ω. The circuit is connected to a 208-V, 60-Hz line. How much resistance should be connected in the circuit to limit the circuit current to a value

Question

The RLC series circuit shown in Figure 24–8 contains an inductor with an inductive reactance of 62 Ω and a capacitor with a capacitive reactance of 38 Ω. The circuit is connected to a 208-V, 60-Hz line. How much resistance should be connected in the circuit to limit the circuit current to a value of 8 A?

Accepted Answer

The first step is to determine the total impedance necessary to limit the circuit current to a value of 8 A:

[latex]Z = \frac{E_{T}}{I_{T}}[/latex]

[latex]Z = \frac{208 V}{8 A}[/latex]

[latex]Z = 26 \Omega[/latex]

The formula for finding impedance in an RLC series circuit can now be adjusted to find the missing resistance value (refer to the Resistive-Inductive-Capacitive Series Circuits section in Appendix B):

[latex]R = \sqrt{Z^{2} - (X_{L} - X_{C})^{2}}[/latex]

[latex]R = \sqrt{(26 \Omega)^{2} - (62 \Omega - 38 \Omega)^{2}}[/latex]

[latex]R = \sqrt{(26 \Omega)^{2} - (24 \Omega)^{2}}[/latex]

[latex]R = \sqrt{100 \Omega^{2}}[/latex]

[latex]R = 10 \Omega[/latex]

Question 24.3: The RLC series circuit shown in Figure 24–8 contains an indu...

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