Concept explainers
For the circuit shown in Fig. 28-14, find (a) its equivalent resistance; (b) the current drawn from the power source; (c) the potential differences across ab, cd, and de; (d) the current in each resistor.
Fig. 28-14
(a)
The net resistance across the circuit provided in the figure 28-14 in the textbook.
Answer to Problem 31SP
Solution:
Explanation of Solution
Given data:
The resistances
The resistances
The resistance across circuit
The voltage across the terminal
Formula used:
The expression for the equivalent resistance in series is written as
Here,
The expression for the equivalent resistance in parallel is written as
Here,
Explanation:
Refer to the fig. 28-14from the textbook.
Draw the circuit diagram:
Since, the resistance
Write the expression for the resistances across
Here,
Substitute
Solve for
Modify the above drawn circuit diagram by using
Understand that the resistors
Here,
Substitute
Here,
Redraw the modified circuit diagram by using the calculated equivalent resistances across the nodes:
Since, all the resisters in the above diagram arein series combination.
Write the expression for the total resistance of the equivalent resistances across
Here,
Substitute
Conclusion:
The net resistance across the point
(b)
The current drawn from the source if the voltage across the circuit is
Answer to Problem 31SP
Solution:
Explanation of Solution
Given data:
Voltage across the circuit is
Formula used:
The expression for theOhm`s law if net current
Explanation:
Redraw the equivalent circuit diagram:
In the above diagram,
Rewrite the expression of the Ohm`s law for the net current across circuit
Here,
Rearrange for
Here,
Substitute
Conclusion:
Therefore, the current drawn from the source is
(c)
The voltage difference across circuits
Answer to Problem 31SP
Solution:
Explanation of Solution
Given data:
The current across
The resistances of the resistor are provided in the figure as
Formula used:
The expression for the net Voltage
Explanation:
The current in the series combination of circuits
Write the expression for the voltage across circuit
Here,
Substitute
Write the expression for the voltage across circuit
Here,
Substitute
Write the expression for the voltage across circuit
Here,
Substitute
Conclusion:
The voltages across circuits
(d)
The current across each resistor if the voltage and current across each circuit are known.
Answer to Problem 31SP
Solution:
Explanation of Solution
Given data:
The voltage across the circuit
The voltage across the circuit
The voltage across the circuit
The current across the circuit
Formula used:
The expression for the net voltage
Explanation:
In this, wewill use the fact that voltage across each resistor in a parallel combination of resistors remains same.
According to the Ohm’s law, the current across the
Rearrange for
Here
Substitute
The voltage across the parallel combination of resistance
Write the expression for the current across
Rearrange for
Here,
Substitute
Write the expression for the current across
Rearrange for
Here,
Substitute
The voltage across the parallel combination of resistors
Write the expression for the current across
Rearrange for
Here,
Substitute
Write the expression for the current across
Rearrange for
Here,
Substitute
Write the expression for the current across
Rearrange for
Here,
Substitute
Conclusion:
The current across the
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Chapter 28 Solutions
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