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Chapter 30: Q90P (page 902)
How long would it take, following the removal of the battery, for the potential difference across the resistor in an RL circuit (with L = 2.00H, R = 3.00) to decay to 10.0% of its initial value?
The time required for the current to decay to 10% of its initial value is t = 1.54s
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Figure (a) shows a circuit consisting of an ideal battery with emf , a resistance R, and a small wire loop of area . For the time interval t = 10 s to t = 20 s, an external magnetic field is set up throughout the loop. The field is uniform, its direction is into the page in Figure (a), and the field magnitude is given by B = at, where B is in Tesla, a is a constant, and t is in seconds. Figure (b) gives the current i in the circuit before, during, and after the external field is set up. The vertical axis scale is set by. Find the constant a in the equation for the field magnitude.
Question: In Figure, a stiff wire bent into a semicircle of radius a = 2.0cmis rotated at constant angular speed in a uniform 20mTmagnetic field. (a) What is the frequency? (b) What is the amplitude of the emf induced in the loop?
In Figure, after switch S is closed at time, the emf of the source is automatically adjusted to maintain a constant current i through S. (a) Find the current through the inductor as a function of time. (b) At what time is the current through the resistor equal to the current through the inductor?
Two coils connected as shown in Figure separately have inductances L1 and L2. Their mutual inductance is M. (a) Show that this combination can be replaced by a single coil of equivalent inductance given by
(b) How could the coils in Figure be reconnected to yield an equivalent inductance of
(This problem is an extension of Problem 47, but the requirement that the coils be far apart has been removed.)
The figure shows two parallel loops of wire having a common axis. The smaller loop (radius r) is above the larger loop (radius R) by a distancex>>R. Consequently, the magnetic field due to the counterclockwise current i in the larger loop is nearly uniform throughout the smaller loop. Suppose that x is increasing at the constant rate. (a)Find an expression for the magnetic flux through the area of the smaller loop as a function of x. (b)In the smaller loop, find an expression for the induced emf. (c)Find the direction of the induced current.
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