The emfs in Figure P29.43 are ε1 = 6.00 V and ε2 = 12.0 V. The resistances are R1 = 15.0 Ω, R2 = 30.0 Ω, R3 = 45.0 Ω, and R4 = 60.0 Ω. Find the current in each resistor when the switch is
- a. open and
- b. closed.
(a)
The current in each resistor when the switch is open.
Answer to Problem 43PQ
The current flowing through the resistor
Explanation of Solution
As the switch is kept open; the current in the wire EFAB will be zero as the circuit is disconnected.
The resistors in the loop BCDEB are connected in series. The current flowing in all the elements in a series circuit is constant.
Write the expression for the equivalent resistance in the loop BCDEB as.
Here,
Write the expression for the current in the loop BCDEB as.
Here,
No current flows through the resistor
Conclusion:
Substitute
Substitute
Thus, the current flowing through the resistor
(b)
The current in each resistor when the switch is closed.
Answer to Problem 43PQ
The current flowing through the resistor
Explanation of Solution
The switch is closed, the current starts flowing through all the resistors in the circuit.
The circuit diagram for the closed switch is shown below.
Write the expression for the Kirchhoff’s voltage law in loop ABCDEFA.
Here,
Write the expression for the Kirchhoff’s voltage law in loop ABEFA.
Write the expression for the current through resistor
Here,
Write the expression for the current through resistor
Here,
Write the expression for the current through resistor
Here,
Write the expression for the current through resistor
Here,
Conclusion:
Substitute
Rearrange the above equation for
Substitute
Substitute
Rearrange the above expression for
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the current flowing through the resistor
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Chapter 29 Solutions
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