
Concept explainers
(a)
The value of current in battery.
(a)

Answer to Problem 100P
The value of current in battery is 25.00 A .
Explanation of Solution
Given:
The value of charge on capacitor is q=1.00 mC .
The value of capacitance is C=5.00 μF .
The emf is ε=310 V .
The current in 50.0 Ω resistor is I50.0 Ω=5.00 A .
The current in R2 resistor is IR2=5.00 A .
Formula used:
By the Kirchhoff’s law, the expression for the current in battery is given as,
Ibattery=I10.0 Ω+I50.0 Ω ..... (1)
Calculation:
The expression for current in 10.0 Ω resistor is,
I10.0 Ω=V10.0 Ω10.0 Ω=1(10.0 Ω)(qC) (∵V10 Ω=qC) ..... (2)
From equation (1) and (2),
Ibattery=1(10.0 Ω)(qC)+I50.0 Ω
The current in battery is calculated as,
Ibattery=1(10.0 Ω)(1.00 mC5.00 μF)+(5.00 A)=1(10.0 Ω)(1.00×10−3 C5.00×10−6 F)+(5.00 A)=25.00 A
Conclusion:
Therefore, the value of current in battery is 25.00 A .
(b)
The value of resistances R1, R2 and R3 .
(b)

Answer to Problem 100P
The value of resistances R1, R2 and R3 are 0.40 Ω , 10.0 Ω and 6.67 Ω respectively.
Explanation of Solution
Formula used:
Apply loop rule to resistors R3 , 50.0 Ω , 5.00 Ω including battery,
ε−(IR1)R1−(I50.0 Ω)(50.0 Ω)−(I5.00 Ω)(5.00 Ω)=0 ..... (1)
Here, IR1=Ibattery=25.0 A
Apply loop rule to resistors 10.0 Ω , 50.0 Ω , R2 including battery,
−(Ibattery−I5.00 Ω)(10.0 Ω)−IR2⋅R2+(I50.0 Ω)(50.0 Ω)=0 ..... (2)
Apply loop rule to resistors R1 , 10.0 Ω , R3 including battery,
ε−(IR1)R1−(Ibattery−I5.00 Ω)(10.0 Ω)−(I10.0 Ω−IR2)R3=0 ..... (3)
Calculation:
From equation (1), the resistance R1 is calculated as,
(310 V)−(25.0 A)R1−(5.00 A)(50.0 Ω)−(10.0 A)(5.00 Ω)=0(25.0 A)R1=10 A⋅ΩR1=1025 ΩR1=0.40 Ω
From equation (2), the resistance R2 is calculated as,
−(25.0 A−5.00 A)(10.0 Ω)−(5.00 A)⋅R2+(5.00 A)(50.0 Ω)=0(5.00 A)⋅R2=50 A⋅ΩR2=10.0 Ω
From equation (3), the resistance R3 is calculated as,
(310 V)−(25 A)(0.40 Ω)−(25 A−5 A)(10.0 Ω)−(20 A−5 A)R3=0(100 A⋅Ω)−(20.0 A−5.00 A)R3=015R3=100 ΩR3=6.666 ΩR3≈6.67 Ω
Conclusion:
Therefore, the value of resistances R1, R2 and R3 are 0.40 Ω , 10.0 Ω and 6.67 Ω respectively.
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Chapter 25 Solutions
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