Figure P29.45 shows five resistors connected between terminals a and b.
- a. What is the equivalent resistance of this combination of resistors?
- b. What is the current through each resistor if a 24.0-V battery is connected across the terminals?
(a)
Find the equivalent resistance of the combination of the resistors.
Answer to Problem 45PQ
The equivalent resistance of the combination is
Explanation of Solution
Consider
Refer to figure above, the resistance
Write the equivalent resistance across the two resistances as.
Here,
Further, the resistances
Write the equivalent resistance across the two resistances as.
Here,
The circuit has
Write the equivalent resistance of the circuit as.
Here,
Conclusion:
Substitute
Rearrange the terms in above equation
Substitute
Rearrange the terms in above equation
Substitute
Thus, the equivalent resistance of the combination is
(b)
Find the current in each resistor in the circuit.
Answer to Problem 45PQ
The current flowing through
Explanation of Solution
Write the expression for the current drawn by the circuit from the battery as.
Here,
Write the expression for the voltage drop across
Here
Write the expression for the voltage drop across
Here
In a parallel connection, the voltage drop across all the elements remains same. Therefore the voltage drop across
Write the expression for the current through
Here
Write the expression for the current through
Here
The resistance
Therefore, the current through the resistance
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
The current through
Substitute
Substitute
Thus, the current flowing through
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Chapter 29 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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