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## Solving Circuit Values

In the circuit shown in Figure 6-14, three resistors having values of 300 , 200 , and 600 are connected in parallel. Total current flow through the circuit is 0.6 A. Find all of the missing values in the circuit. Solution:
The first step is to find the total resistance of the circuit. The reciprocal formula will be used. Now that the total resistance of the circuit is known, the voltage applied to the circuit can be found by using the total current value and Ohm’s Law. One of the rules for parallel circuits states that the voltage across all of the parts of a parallel circuit is the same as the total voltage. Therefore, the voltage drop across each resistor is 60 V, Figure 6-15.  Since the voltage drop and resistance of each resistor is known, Ohm’s Law can be used to determine the amount of current flow through each resistor, Figure 6-16  The amount of power (watts) used by each resistor can be found by using Ohm’s Law. A different formula will be used to find the amount of electrical energy converted into heat by each of the resistors. In Unit 5, it was stated that the total amount of power in a circuit is equal to the sum of the power used by all the parts. This is true for any type of circuit. Therefore, the total amount of power used by this circuit can be found by taking the sum of the power used by all resistors, Figure 6-17. In the circuit shown in Figure 6-18, three resistors are connected in parallel. Two of the resistors have a value of 900 and 1800 .  Example 2 The value of the resistor R2 is unknown. The total resistance of the circuit is 300 . Resistor R2 has a current flow through it of 0.2 A. Find the missing circuit values. Solution:
The first step in solving this problem is to find the missing resistor value. This can be done by changing the reciprocal formula as shown:

or One of the rules for parallel circuits states that the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistors. Therefore, the reciprocal of any individual resistor is equal to the difference between the reciprocal of the total resistance and the sum of the reciprocals of the other resistors in the circuit. Now that the resistance of resistor R2 has been found, the voltage
drop across resistor R
2 can be determined using the current flow through
the resistor and Ohm’s Law,
Figure 6-19. If 120 volts is dropped across resistor R2, the same voltage is dropped
across each component of the circuit. Now that the voltage drop across each part of the circuit is known
and the resistance is known, the current flow through each branch can
be determined using Ohm’s Law,
Figure 6-20.   If the wattage values of the three resistors are added to compute total power for the circuit, it will be seen that their total is 47.92 W instead of the computed 48 W. The small difference in answers is caused by the rounding off of other values. In this instance, the current of resistor Rwas rounded from 0.066666666 to 0.066.

In the circuit shown in Figure 6-22, three resistors are connected in parallel. Resistor R1 is producing 0.075 W of heat, R2 is producing 0.45 W of heat, and R3 is producing 0.225 W of heat. The circuit has a total current of 0.05 A.

Solution:

Since the amount of power dissipated by each resistor is known, the total power for the circuit can be found by taking the sum of the power used by each component.   SUMMARY

1.  A parallel circuit is characterized by the fact that it has more than
one path for current flow.
2.  Three rules for solving parallel circuits are:
A. The total current is the sum of the currents through each individual branch of the circuit.
B. The voltage is the same across any part of the circuit.
C. The reciprocal of total resistance is the sum of the reciprocals of each individual branch.
3. Circuits in homes are connected in parallel.
4. The total power in a parallel circuit is equal to the sum of the
power dissipation by each component.

REVIEW QUESTIONS

1. What characterizes a parallel circuit?
2.  Why are circuits in homes connected in parallel?
3.  State three rules concerning parallel circuits.
4. A parallel circuit contains four branches. One branch has a current flow of 0.8 A, another has a current flow of 1.2 A, the third has a current flow of 0.25 A, and the fourth has a current flow of 1.5 A. What is the total current flow in the circuit?
5. Four resistors having a value of 100 each are connected in parallel. What is the total resistance of the circuit?
6. A parallel circuit has three branches. An ammeter is connected in series with the output of the power supply and indicates a total current flow of 2.8 A. If branch 1 has a current flow of 0.9 A and branch 2 has a current flow of 1.05 A, what is the current flow through branch 3?
7. Four resistors having values of 270 , 330 , 510 , and 430 are connected in parallel. What is the total resistance of the circuit?
8. A parallel circuit contains four resistors. The total resistance of the circuit is 120 . Three of the resistors have values of 820.

## PARALLEL CIRCUITS

1. Find the missing values in the circuit shown in Figure 6-26.      