Question

an inductor is connected to a 20.0 hz power supply that produces a 56.0 v rms voltage. what inductance is needed to keep the instantaneous current in the circuit below 70.0 ma? h

Answer 1

To keep the instantaneous current in the circuit below 70.0 mA, an inductor with a very high inductance value is needed.

Step-by-step explanation:

To find the inductance needed to keep the instantaneous current in the circuit below 70.0 mA, we can use the formula:

V = L * di/dt

Where:

• V is the voltage
• L is the inductance
• di/dt is the rate of change of current

In this case, the voltage is 56.0 V rms, or approximately 79.1 V peak. The current we want to keep below is 70.0 mA, or 0.07 A. The rate of change of current is approximately 0, since we want to keep it constant. So:

79.1 V = L * 0

Since the rate of change of current is 0, the inductance needed is infinite. In practical terms, to keep the current constant below 70.0 mA, we would need an inductor with a very high inductance value.

Answer 2

To calculate the inductance needed to keep the instantaneous current below 70.0 mA, use the formula I = V / (ωL), where I is the maximum current, V is the voltage, ω is the angular frequency, and L is the inductance. Plugging in the given values, the inductance needed is approximately 2.8 mH.

Step-by-step explanation:

To calculate the inductance needed to keep the instantaneous current in the circuit below 70.0 mA, we can use the formula:

I = V / ωL

Where:

• I is the maximum current
• V is the voltage
• ω is the angular frequency, which can be calculated as 2πf
• L is the inductance

Plugging in the values given:

I = 70.0 mA = 0.07 A

V = 56.0 V

ω = 2π(20.0 Hz) = 40π

Solving for L:

0.07 A = 56.0 V / (40πL)

L = 56.0 V / (0.07 A * 40π)

L ≈ 2.8 mH