Critical Damping A motor coil having an inductance of 8 H is in parallel with a 2 µF 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 a. (c) Write the equation for the current flowing into the resistor i the top node is labeled v, the bottom node is grounded, and v = Rir. (d) Verify that your equation is a solution to the circuit differential equation, dir dt + 2a + a²i₁ = 0 dir dt

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Critical Damping
A motor coil having an inductance of 8 H is in parallel with a 2 µF 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 a. (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 = Rir. (d) Verify
that your equation is a solution to the circuit differential equation,
dir
dt
+ 2a
dir
dt
+ a²i, = 0
Transcribed Image Text:Critical Damping A motor coil having an inductance of 8 H is in parallel with a 2 µF 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 a. (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 = Rir. (d) Verify that your equation is a solution to the circuit differential equation, dir dt + 2a dir dt + a²i, = 0
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