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In the combination of 12 Ω resistors shown in the diagram, there are two different parallel combinations that, in turn, are in series with the middle resistor.
a. What is the resistance of each of the two parallel combinations?
b. What is the total equivalent resistance between points A and B?
c. If there is a voltage difference of 18 V between points A and B, what is the current flowing through the entire combination?
d. What is the current flowing through each of the resistors in the three-resistor parallel combination?
(a)
The equivalent resistance of the two parallel segments.
Answer to Problem 4SP
The current through the circuit is
Explanation of Solution
Given info: The given circuit is shown below.
Write the formula for the resultant resistance of two equal resistors connected in parallel.
Here,
Substitute
Write the formula for the resultant resistance of three equal resistors connected in parallel.
Here,
Substitute
Conclusion:
The equivalent resistance of the two parallel connections in the arrangement is
(b)
The equivalent resistance between point A to B.
Answer to Problem 4SP
The overall resistance between points A and B is
Explanation of Solution
Given info: The given circuit is shown below.
In this arrangement the two parallel segments and one
Write the formula for the equivalent resistance between point A and B.
Here,
Substitute
Conclusion:
The overall resistance between points A and B is
(c)
The current flowing through the circuit.
Answer to Problem 4SP
The current in the circuit is
Explanation of Solution
Given info: The voltage difference between point A and B is
Write the formula for current.
Here,
From section (b) the overall resistance between points A and B is
Substitute
Conclusion:
The current in the circuit is
(d)
The current flowing through the individual resistors in the three-resistor parallel combination.
Answer to Problem 4SP
The current flowing through the individual resistors in the three-resistor parallel combination is
Explanation of Solution
Given info: The given circuit is shown below.
The current through all the segments will be same. From section (c) the current in the circuit is
The current through each segment of a parallel connection of resistors depends on the resistance of each resistor. Since the resistance of the three resistors is same, equal current will pass through the individual resistor which is one third of the total current.
Write the formula for the current through each of the resistor in the three-resistor parallel segment.
Here,
Substitute
Conclusion:
The current flowing through the individual resistors in the three-resistor parallel combination is
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