Three resistors with resistances R1 = R/2 and R2 = R3 = R are connected as shown, and a potential difference of 225 V is applied across terminals a and b (Fig. P29.49).
a. If the resistor R1 dissipates 75.0 W of power, what is the value of R?
b. What is the total power supplied to the circuit by the emf?
c. What is the potential difference across each of the three resistors?
(a)
Find the value of resistance from the given circuit.
Answer to Problem 49PQ
The value of
Explanation of Solution
Refer the figure
Write the equivalent resistance of the parallel circuit as.
Here
Since
Write the equivalent resistance of circuit as.
Here,
Write the expression for the current drawn by the circuit from the voltage applied as.
Here
Write the expression for power dissipated across
Here,
Conclusion:
Substitute
Rearrange the terms in above equation
Substitute
Substitute
Substitute
Rearrange the terms in above equation
Thus, the value of
(b)
Find the total power supplied to the circuit.
Answer to Problem 49PQ
The total power supplied to the circuit is
Explanation of Solution
The total power supplied to the circuit is given as
Here
Conclusion:
Substitute
Substitute
Thus, the total power supplied to the circuit is
(c)
Find the potential difference across the three resistors.
Answer to Problem 49PQ
The potential difference across the resistance
Explanation of Solution
Write the expression for the potential difference across the resistance
Here
Write the expression for the remaining potential drop is across the parallel combination of
Here
Conclusion:
Substitute
Substitute
Thus, the potential difference across the resistance
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Chapter 29 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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