For such a connection, the current is the same for all individual resistors and

Question

For such a connection, the current is the same for all individual resistors and the total voltage is the sum of the voltages across the individual resistors.

Using Ohm's law (R=VI), one can show that, for a series connection, the equivalent resistance is the sum of the individual resistances.

Mathematically, these relationships can be written as:

I=I1=I2=I3=...

V=V1+V2+V3+...

Req?series=R1+R2+R3+...

An example of a parallel connection is shown in the diagram:

(Figure 2)

For resistors connected in parallel the voltage is the same for all individual resistors because they are all connected to the same two points (A and B on the diagram). The total current is the sum of the currents through the individual resistors. This should makes sense as the total current "splits" at points A and B.

Using Ohm's law, one can show that, for a parallel connection, the reciprocal of the equivalent resistance is the sum of the reciprocals of the individual resistances.

Mathematically, these relationships can be written as:

V=V1=V2=V3=...

I=I1+I2+I3+...

1Req?parallel=1R1+1R2+1R3+...

NOTE: If you have already studied capacitors and the rules for finding the equivalent capacitance, you should notice that the rules for the capacitors are similar - but not quite the same as the ones discussed here.

In this problem, you will use the the equivalent resistance formulas to determine Req for various combinations of resistors.

Part A

For the combination of resistors shown, find the equivalent resistance between points A and B.

(Figure 3)

Express your answer in Ohms.

Part B

For the set-up shown, find the equivalent resistance between points A and B.

(Figure 4)

Explanation / Answer

Part A : Figure 3.

Equivalent resistance = R = R1 +R2 +R3 = 2 + 3 + 4 = 9 ohm

Part A : Figure 4.

Equivalent resistance = R = R1*R2/(R1 +R2) = 6*3/(6 + 3) = 2 ohm

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