a.
The equivalent resistance of the parallel circuit.
a.
Answer to Problem 15PP
The equivalent resistance of the network is
Explanation of Solution
Given:
A parallel circuit consisting of two resistors of value 15 Ω each and third resistor being 10 Ω are connected across a 30-V battery.
Formula used:
The equivalent resistance of a parallel branch of two resistances is given by,
Calculation:
Consider the circuit shown in Figure 1.
Figure 1
Here, the equivalent resistance of the parallel branches can be calculated using (1) as,
With reference to the case when all the resistance values were 15 Ω, the equivalent resistance decreases slightly when one of the resistances is decreased to 10 Ω.
Conclusion:
The equivalent resistance of the circuit is
b.
The current in the circuit
b.
Answer to Problem 15PP
The current through the circuit is
Explanation of Solution
Given:
A parallel circuit consisting of two resistors of value 15 Ω each and third resistor being 10 Ω are connected across a 30-V battery.
Formula used:
For the resistance of the circuit and supply voltage, the current can be calculated using the Ohm’s law as,
Calculation:
The current flowing through the circuit can be calculated by using the relation in (2), by substituting the total resistance obtained in the part a and the supply voltage V=30 V, as
With reference to the case when all the resistance values were 15 Ω, the total current increases by 1 A when one of the resistances is decreased to 10 Ω.
Conclusion:
The current through the circuit is 7 A.
c.
To explain: The effect of change in current through 15 Ω due to a given change in resistance of the circuit.
c.
Answer to Problem 15PP
The current flowing through 15 Ω branch does not change and it remains as 2 A.
Explanation of Solution
Given:
A parallel circuit consisting of two resistors of value 15 Ω each and third resistor being 10 Ω are connected across a 30-V battery.
Formula used:
The voltage in the each branch in a parallel circuit is equal. The current flowing through each of the branch is expressed in terms of the supply voltage and their individual resistance values as,
Calculation:
Here, consider the first branch consisting of 10 Ω, the current flowing through it is,
Now, the current through the two branches with 15 Ω are equal and can be calculated as,
It can be observed that, the current through the 15 Ω remains the same though the total current shows an increase in value.
Conclusion:
The current in 15Ω remains the same as when the circuit has all resistance values as 15 Ω.
Chapter 23 Solutions
Glencoe Physics: Principles and Problems, Student Edition
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