1. Design a solenoid that will produce a magnetic field of 0.047 T using a curre

Question

1. Design a solenoid that will produce a magnetic field of 0.047 T using a current I = 24 A. If the radius of the solenoid is 5 cm and the solenoid is 4.1 m long, how many turns of wire are required?

2. Use the exact values you enter in previous answer(s) to make later calculations.

The battery in the figure below is a real battery. That is, it has some internal resistance Rint in series with an ideal battery with an emf of V0. In an attempt to determine Rintand V0, a resistor

R1 = 700 ?

is first placed across points A and B, and the voltage across the resistor is measured to be 5.0 V. This resistor is then replaced with a second resistor with

R2 = 2,400 ?,

and the voltage across R2 is found to be 9.8 V. Find Rint and V0.

(a) Express the resistors in parallel as a single equivalent resistor. What is the value of this resistor?
?

(b) Combine this equivalent resistor with R1 to get the total equivalent resistance of the circuit. What is the value of this resistor?
?

(c) The circuit is now "reduced" to a battery in series with a single equivalent resistance. Use your result from part (b) to find the current through the battery and resistor R1.
A

4.

Consider the circuit in the figure below with resistors R1 = 540 ?, R2 = 430 ?, R3 = 280 ?, and R4 = 186 ?.

What is the equivalent resistance between points A and B?
?

Rint = ? V0 = V 2. Use the exact values you enter in previous answer(s) to make later calculations. The battery in the figure below is a real battery. That is, it has some internal resistance Rint in series with an ideal battery with an emf of V0. In an attempt to determine Rintand V0, a resistor R1 = 700 ? is first placed across points A and B, and the voltage across the resistor is measured to be 5.0 V. This resistor is then replaced with a second resistor with R2 = 2,400 ?, and the voltage across R2 is found to be 9.8 V. Find Rint and V0. Rint = ? V0 = V (a) Express the resistors in parallel as a single equivalent resistor. What is the value of this resistor? ? (b) Combine this equivalent resistor with R1 to get the total equivalent resistance of the circuit. What is the value of this resistor? ? (c) The circuit is now reduced to a battery in series with a single equivalent resistance. Use your result from part (b) to find the current through the battery and resistor R1. A 4. Consider the circuit in the figure below with resistors R1 = 540 ?, R2 = 430 ?, R3 = 280 ?, and R4 = 186 ?. What is the equivalent resistance between points A and B? ? e 1 = 1.6 V. Analyze the circuit in the figure below. 3. Assume the resistance values are R1 = 2,700 ?, R2 = 1,800 ?, R3 = 4,400 ?, and the battery emf is

Explanation / Answer

1.

Magnetic field due to a solenoid is

B=uoN*I/L

=>N=B*L/uo*I =0.047*4.1/(4pi*10-7)*24

N=6390 turns

2.

at V=5 volts and R1=700 ohms

I=V/R =5/700=7.143*10-3 A

Emf

Vo=V+IRint

Vo=5+(7.143*10-3)Rint

Vo-(7.143*10-3)Rint=5-------------------1

at V=9.8 V and R=2400 ohms

I=V/R =9.8/2400 =4.083*10-3 A

Emf

Vo=9.8+(4.083*10-3)Rint

Vo-(4.083*10-3)Rint=9.8---------------2

solving 1 and 2 we get

Vo=16.2 Volts

Rint=1568.63 ohms

3)

a)

1/R23=1/R2+1/R3 =1/1800 +1/4400

R23=1277.42 ohms

b)

equivalent resistance

Req=R1+R23=2700+1277.42

Req=3977.42 ohms

c)

I=E/Req=1.6/3977.42

I=4.02*10-4 A or 0.402 mA

4)

R2 and R4 are in series

R24=430+186=616 ohms

R3 and R24 are in parallel

1/R234=1/616+1/280

R234=192.5 ohms

R1 and R234 are in series ,so equivalent resistance

Req=540+192.5=732.5 ohms

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