PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
6th Edition
ISBN: 9781429206099
Author: Tipler
Publisher: MAC HIGHER
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Chapter 25, Problem 100P

(a)

To determine

The value of current in battery.

(a)

Expert Solution
Check Mark

Answer to Problem 100P

The value of current in battery is 25.00A .

Explanation of Solution

Given:

The value of charge on capacitor is q=1.00mC .

The value of capacitance is C=5.00μF .

The emf is ε=310V .

The current in 50.0Ω resistor is I50.0Ω=5.00A .

The current in R2 resistor is IR2=5.00A .

Formula used:

By the Kirchhoff’s law, the expression for the current in battery is given as,

  Ibattery=I10.0Ω+I50.0Ω ..... (1)

Calculation:

The expression for current in 10.0Ω resistor is,

  I10.0Ω=V 10.0Ω10.0Ω=1( 10.0Ω)(qC)(V 10Ω=qC) ..... (2)

From equation (1) and (2),

  Ibattery=1(10.0Ω)(qC)+I50.0Ω

The current in battery is calculated as,

  Ibattery=1( 10.0Ω)( 1.00mC 5.00μF)+(5.00A)=1( 10.0Ω)( 1.00× 10 3 C 5.00× 10 6 F)+(5.00A)=25.00A

Conclusion:

Therefore, the value of current in battery is 25.00A .

(b)

To determine

The value of resistances R1,R2 and R3 .

(b)

Expert Solution
Check Mark

Answer to Problem 100P

The value of resistances R1,R2 and R3 are 0.40Ω , 10.0Ω and 6.67Ω respectively.

Explanation of Solution

Formula used:

Apply loop rule to resistors R3 , 50.0Ω , 5.00Ω including battery,

  ε(IR1)R1(I50.0Ω)(50.0Ω)(I5.00Ω)(5.00Ω)=0 ..... (1)

Here, IR1=Ibattery=25.0A

Apply loop rule to resistors 10.0Ω , 50.0Ω , R2 including battery,

  (IbatteryI5.00Ω)(10.0Ω)IR2R2+(I50.0Ω)(50.0Ω)=0 ..... (2)

Apply loop rule to resistors R1 , 10.0Ω , R3 including battery,

  ε(IR1)R1(IbatteryI5.00Ω)(10.0Ω)(I10.0ΩIR2)R3=0 ..... (3)

Calculation:

From equation (1), the resistance R1 is calculated as,

  (310V)(25.0A)R1(5.00A)(50.0Ω)(10.0A)(5.00Ω)=0(25.0A)R1=10AΩR1=1025ΩR1=0.40Ω

From equation (2), the resistance R2 is calculated as,

  (25.0A5.00A)(10.0Ω)(5.00A)R2+(5.00A)(50.0Ω)=0(5.00A)R2=50AΩR2=10.0Ω

From equation (3), the resistance R3 is calculated as,

  (310V)(25A)(0.40Ω)(25A5A)(10.0Ω)(20A5A)R3=0(100AΩ)(20.0A5.00A)R3=015R3=100ΩR3=6.666ΩR36.67Ω

Conclusion:

Therefore, the value of resistances R1,R2 and R3 are 0.40Ω , 10.0Ω and 6.67Ω respectively.

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Chapter 25 Solutions

PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS

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