A motor coil having an inductance of 8 H is in parallel with a 2 F capacitor and a

Chapter 9, Problem 21

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A motor coil having an inductance of 8 H is in parallel with a \(2\ \mu F\) capacitor and a resistor of unknown value. The response of the parallel combination is determined to be critically damped. (a) Determine the value of the resistor. (b) Compute \(\alpha\). (c) Write the equation for the current flowing into the resistor if the top node is labeled v, the bottom node is grounded, and \(v = Ri_r\). (d) Verify that your equation is a solution to the circuit differential equation,

\(\frac{d i_{r}}{d t}+2 \alpha \frac{d i_{r}}{d t}+\alpha^{2} i_{r}=0\)

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