Question

Find the voltages across a 2-H inductor for currents of (a) 10 A, (b) 10 sin (377t+10) A, and (c) 10 cos (104t-20) A. As always, assume associate references because there is no statement to the contrary.

Answer 1

To find the voltage across a 2-H inductor for various currents, use v(t) = L*(di/dt). For constant current, the voltage is 0 V. For oscillating currents, take the derivative of the current expression and multiply by the inductor's value for the voltage v(t).

Step-by-step explanation:

The student is asking how to find the voltages across a 2-H inductor when there are different types of currents passing through it. The formulas needed are derived from the basic relationship between voltage (v(t)), inductance (L), and the rate of change of current (di/dt) in the inductor: v(t) = L*(di/dt).

1. For a constant current of 10 A, since the current does not change with time (di/dt = 0), the voltage across the inductor is 0 V.
2. For a sinusoidal current i(t) = 10 sin(377t+10) A, we differentiate this with respect to t to get the rate of change of current di/dt which gives us 3770 cos(377t+10) A/s. Multiplying this by the inductance L (2 H) gives us the voltage v(t) = 7540 cos(377t+10) V.
3. Lastly, for the current i(t) = 10 cos(104t-20) A, differentiating this yields -1040 sin(104t-20) A/s, and multiplying by the inductance L (2 H) results in v(t) = -2080 sin(104t-20) V.

In each case, you take the derivative of the current with respect to time and multiply by the induction value to find the voltage across the inductor for varying types of currents.