A battery with ε = 6.00 V and no internal resistance supplies current to the circuit shown in Figure P27.9. When the double-throw switch S is open as shown in the figure, the current in the battery is 1.00 mA. When the switch is closed in position a, the current in the battery is 1.20 mA. When the switch is closed in position b, the current in the battery is 2.00 mA. Find the resistances (a) R1, (b) R2, and (c) R3.
Figure P27.9 Problems 9 and 10.
(a)
Answer to Problem 28.11P
Explanation of Solution
Given information: Emf across the battery is
Explanation:
When the switch S is open, then the three resistors
Formula to calculate the equivalent resistance across the circuit, when the switch S is open.
Here,
As the total emf across the battery is equal to the voltage across the battery.
Here,
Substitute
Formula to calculate the equivalent resistance across the circuit, when the switch S is open.
Here,
Substitute
Substitute
When the switch is closed in position
From equation (2), formula to calculate the equivalent resistance across the circuit, when the switch is closed in position
Here,
Formula to calculate the resistance when the resistors are connected in parallel.
From equation (3), formula to calculate the equivalent resistance across the circuit, when the switch is closed in position
Substitute
Substitute
Substitute
When the switch is closed in position
From equation (2), formula to calculate the equivalent resistance across the circuit, when the switch is closed in position
Here,
From equation (3), formula to calculate the equivalent resistance across the circuit, when the switch is closed in position
Substitute
Substitute
Subtract equation (14) from (5) to find
Thus, the value of the resistance
Subtract equation (14) from (10) to find
Substitute
Thus, the value of the resistance
Substitute
Thus, the value of the resistance
Conclusion:
Therefore, the value of the resistance
(b)
Answer to Problem 28.11P
Explanation of Solution
Given information: Emf across the battery is
Explanation:
From part (a) equation (17), the value of resistance
Thus, the value of the resistance
Conclusion:
Therefore, the value of the resistance
(c)
Answer to Problem 28.11P
Explanation of Solution
Given information: Emf across the battery is
Explanation:
From part (a) equation (15), the value of resistance
Thus, the value of the resistance
Conclusion:
Therefore, the value of the resistance
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Chapter 28 Solutions
PHYSICS:F/SCI.+.,V.2-STUD.S.M.+STD.GDE.
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- You connect a battery, resistor, and capacitor as in (Figure 1), where R = 14.0 Ω and C = 3.00 ×10^-6 F. The switch S is closed at t = 0. When the current in the circuit has magnitude 3.00 A, the charge on the capacitor is 40.0 × 10^−6 C. At what time t after the switch is closed is the charge on the capacitor equal to 40.0 x 10^-6 C? When the current has magnitude 3.00 A, at what rate is energy being stored in the capacitor?arrow_forwardIf you have a circuit like the one in the figure with E=51.0V, R1=793.2Ω, R2=781.3Ω, R3=534.9Ω and R4=793.2Ω, determine the current in amps passing through the resistor R1 (Write your answer to 3 significant figures)arrow_forwardSwitch S shown in Figure P28.71 has been closed for a long lime, and the electric circuit carries a constant current. Take C1 = 3.00 μF, C2 = 6.00 μF, R1 = 4.00 kΩ, and R2 , = 7.00 kΩ. The power delivered to R2 , is 2.40 W. (a) Find the charge on C1 . (b) Now the switch is opened. After many milliseconds, by how much has the charge on C2 changed?arrow_forward
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