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Chapter 30: Q73P (page 900)

Two coils are at fixed locations. When coil 1 has no current and the current in coil 2 increases at the rate 15.0 A/s, the emf in coil 1 is 25.0 mV. (a) What is their mutual inductance? (b) When coil 2 has no current and coil 1 has a current of 3.60A, what is the flux linkage in coil 2?

Short Answer

Expert verified

a) $M = 1.67 脳 10^{- 3} H$

b) $蠒_{21} = 6.0 脳 10^{- 3} W b$

Step by step solution

01

Given

Rate of change of current,

$\frac{d i_{2}}{d t} = 15.0 A / s 蔚_{1} = 25.0 m V = 25.0 脳 10^{- 3} V I_{1} = 3.6 A$

02

Understanding the concept

We have the formula for the mutual inductance induced in the coil, we also have enough information given, so we can calculate the mutual inductance. We also have enough information along with the formula for flux linkage, so we can find the required answer.

Formula:

$蠒 = \frac{M I}{N}$

$M = \frac{蔚}{|d i / d t|}$

03

(a) Calculate the mutual inductance

We have,

$M = \frac{蔚}{|\frac{d i}{d t}|}$

So, mutual inductance in coil 1 will become,

$M = \frac{蔚}{|\frac{d i}{d t}|} M = \frac{25.0 脳 10^{- 3}}{15} M = 1.67 + 10^{- 3} H$

04

(b) Calculate the flux linkage in coil 2 when coil 2 has no current and coil 1 has a current of 3.60 A

We have,

$蠒 = \frac{M I}{N}$

Here, N=1

$蠒_{21} = \frac{M I_{1}}{N} 蠒_{21} = \frac{1.67 脳 10^{- 3} 脳 3.6}{1} 蠒_{21} = 6.0 脳 10^{- 3} W b$

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Most popular questions from this chapter

Two solenoids are part of the spark coil of an automobile. When the current in one solenoid falls from $6.0 A$ to zero in 2.5ms, an emf of 30 kVis induced in the other solenoid. What is the mutual inductance M of the solenoids?

A uniform magnetic field is perpendicular to the plane of a circular wire loop of radius r. The magnitude of the field varies with time according to $B = B_{0} e^{(- \frac{t}{蟿})}$ , where $B_{0}$ and $蟿$ are constants. Find an expression for the emf in the loop as a function of time.

In Figure, a 120 turncoil of radius 1.8 cm and resistance $5.3 惟$ is coaxial with a solenoid of 220 turne/cm and diameter 3.2 cm. The solenoid current drops from 1.5 Ato zero in time interval $鈭� t = 25 m s$ . What current is induced in the coil during $鈭� t$ ?

A rectangular coil of N turns and of length a and width b is rotated at frequency f in a uniform magnetic field, as indicated in Figure. The coil is connected to co-rotating cylinders, against which metal brushes slide to make contact. (a) Show that the emf induced in the coil is given (as a function of time t) by $蔚 = 2 蟿蟿 f N a b s i n (2 蟿蟿 f t) = 蔚_{0} s i n (2 蟿蟿 f t)$ . This is the principle of the commercial alternating-current generator. (b) What value of Nabgives an emf with $蔚_{0} 150 V$ when the loop is rotated at $60.0 \frac{rev}{s}$ in a uniform magnetic field of 0.500 T?

Suppose the emf of the battery in the circuit shown in Figure varies with time t so that the current is given by i(t) = 3.0 +5.0 t , where i is in amperes and t is in seconds. Take $R = 4.0 惟 a n d L = 5.0 H$ , and find an expression for the battery emf as a function of t. (Hint: Apply the loop rule.)

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