A parallel circuit is one in which there is more than one path for current. Parallel circuits can be thought of as two parallel lines, representing conductors, with a voltage source and components connected between the lines. This idea is illustrated in Figure 3-14. The source voltage appears across each component. Each path for current is called a branch. The current in any branch is dependent only on the resistance of that branch and the source voltage.
Figure 3-14
As more branches are added to a parallel circuit, the total resistance decreases. This is easy to see if you consider each added path in terms of conductance. Recall that conductance is the reciprocal of resistance. As parallel branches are added, new paths are provided for current, increasing the conductance. There is more total current in the circuit. If the total current in a circuit increases, with no change in source voltage, the total resistance must decrease according to Ohm's Law. The total conductance of a parallel circuit is the sum of the individual conductances. This can be written:
By substituting the definition for resistance into the formula for conductance, the reciprocal formula for resistance in parallel circuits is obtained. It is:
In parallel circuits, there are junctions where two or more components are connected. Figure 3-15 shows a circuit node labelled A. 
Figure 3-14
Since electrical charge cannot accumulate at a point, the current into the junction must be equal to the current from the junction. This idea is expressed in Kirchhoff's Current Law, which is stated as:
KCL: The sum of the currents entering a circuit node is equal to the sum of the currents leaving the node.
One important idea can be seen by applying Kirchhoff's Current Law to a point next to the source voltage. The current leaving the source must be equal to the sum of the individual branch currents.
In section 2 Series Circuits, you observed how a series circuit causes voltage to be divided between the various resistances. In parallel circuits, it is the current that is divided between the resistances. Keep in mind that the larger the resistance, the smaller the current. The general current divider rule can be written:
where 𝐺𝑥 is the conductance of the parallel branch under consideration, 𝐺𝑇 is the total conductance of the parallel branches, and 𝐼𝑇 is the total current entering the part of the circuit that consists of parallel branches. Note that this is the dual of the voltage divider rule.
Notice that the fraction 𝑅𝑇𝑅𝑥 is always less than 1.0 and represents the fraction of the total current in 𝑅𝑥. This equation can be simplified for the special case of exactly two resistors. The special two-resistor current divider rules are written:
Parallel Circuits
Measure the resistors with listed values in Table 3-10.
Table 3-10
Component
Listed
Value
Measured
Value
R1
2.7 kΩ
R2
4.7 kΩ
R3
8.2 kΩ
R4
10 kΩ
In Table 3-11 you will tabulate the total resistance as resistors are added in parallel. (Parallel connections are indicated with two parallel lines shown between the resistors.) Enter the measured value of 𝑅1 in the table.
Table 3-11
R1
R1||R2
R1||R2||R3
R1||R2||R3||R4
RT (measured)
 Then connect 𝑅2 in parallel with 𝑅1 and measure the total resistance as shown in Figure 3-16. Enter the measured
resistance of  𝑅1 in parallel with 𝑅2 in Table 3-10.
Figure 3-16
Add  𝑅3 in parallel with 𝑅1 and 𝑅2. Measure the parallel resistance of all three resistors. Then add 𝑅4 in parallel with the other three resistors and repeat the measurement. Record your results in Table 3-11.
Complete construction of the parallel circuit by adding the voltage source and the ammeter as shown in Figure 3-17.
Figure 3-17
Be certain that the ammeter is connected in series with the voltage source as shown.
Measure the total current in the circuit and record it below.
IT (measured)
Measure the voltage across each resistor. How does the voltage across each resistor compare to the source voltage?
Use Ohm's Law to compute the branch current in each resistor. Use the source voltage and the measured resistances. Tabulate the computed currents in Table 3-12.
Table 3-12
I (computed)
Use the general current divider rule to compute the current in each branch. Use the total current that you measured in step 6 and the total resistance that you recorded in Table 3-11, column 5. Compare the calculation using the current divider rule with the results using Ohm's Law. Show your results in Table 3-13.
Table 3-13
I (computed)
Prove Kirchhoff's Current Law for the circuit by showing that the total current is equal to the sum of the branch currents:
Simulate a burned-out resistor (which is effectively an open-circuit) by removing R4 from the circuit. What is the new total current?
IT =