Question

there exists a circuit that has an unknown equivalent resistance, an equivalent inductance of 25 mh, and an equivalent capacitance of 20 nf. what value of resistance would result in the circuit being critically damped?

Answer 1

The resistance required to achieve critical damping for a circuit with an equivalent inductance of 25 mH and an equivalent capacitance of 20 nF is approximately 70.72 ohms.

Step-by-step explanation:

To determine the value of resistance that would result in an RLC circuit being critically damped, one must use the critical damping condition which involves the resistance (R), inductance (L), and capacitance (C) of the circuit. To achieve critical damping, the resistance should be equal to the critical resistance Rc, given by Rc = 2 * sqrt(L/C), where L is the inductance and C is the capacitance. The provided equivalent inductance is 25 mH (millihenrys) or 25 x 10-3 H, and the equivalent capacitance is 20 nF (nanofarads) or 20 x 10-9 F.

Critically Damped Resistance
Rc = 2 * sqrt(L/C)
= 2 * sqrt((25 x 10-3 H) / (20 x 10-9 F))
= 2 * sqrt(1250)
= 2 * 35.36
= 70.72 ohms

Therefore, the resistance required for critical damping in the circuit is approximately 70.72 ohms.