Question

Tal wirid thin imannitude of the industed enit at f ai 1,60 s. inv thi Find the madilisde of llie induced eint at f=4.00. riv) Jet ar withat time is the eint aero? The current in a 40.0=mH inductor changes with time as i=4.00t²−8.00ξ, where i is in amperes and t is in seconds,

(a) Find the magnitude of the induced emf at t=1.00.5. mV
(b) Find the magnitude of the induced ernf at t=4.00 si Check your calculation of the derivative of the current, mV
(c) At what time is the emf zero?

Answer 1

The magnitude of the induced emf at t = 1.00 is 0.16 V and at t = 4.00 is -1.28 V. The emf is zero at t = 0 s and t = 4.00 s.

Step-by-step explanation:

In order to find the magnitude of the induced emf at t = 1.00, we can substitute the value of t into the equation i = 4.00t² - 8.00t. Plugging in t = 1.00, we get i = 4.00(1.00)² - 8.00(1.00) = -4.00 A. The magnitude of the induced emf can be calculated using the formula E = -L(di/dt), where L is the self-inductance of the inductor. Since the given value is in mH, we need to convert it to H by dividing by 1000. E = -0.040*(-4.00) = 0.16 V.

At t = 4.00, we can again substitute the value of t into the equation i = 4.00t² - 8.00t. Plugging in t = 4.00, we get i = 4.00(4.00)² - 8.00(4.00) = 32.00 A. Using the same formula E = -L(di/dt), we can calculate the magnitude of the induced emf. E = -0.040*(32.00) = -1.28 V.

To find the time at which the emf is zero, we need to solve the equation i = 0. Setting i = 0 in the equation i = 4.00t² - 8.00t, we have 4.00t² - 8.00t = 0. Factoring out a t, we get t(4.00t - 8.00) = 0. So t = 0 or 4.00. Therefore, at t = 0 s and t = 4.00 s, the emf is zero.