Question

Two resistors are connected in parallel.

a.) If a third resistor is now connected in parallel with the original two, does the equivalent resistance of the circuit increase, decrease, or remain the same?

b.) Choose the best explanation from among the following:

1. The third resistor gives yet another path for current to flow in the circuit, which means that the equivalent resistance is less.

2. Adding a resistor generally tends to increase the resistance, but putting it in parallel tends to decrease the resistance; therefore the effects offset and the resistance stays the same.

or 3. Adding more resistance to the circuit will increase the equivalent resistance.

Answer 1

When Resistors are connected in parallel, then their equivalent resistance is given by:

1/Req = 1/R1 + 1/R2 + 1/R3

For ease of calculations, assume that each resistor have 'R' resistance.

when two resistors are in parallel, then

1/R1eq = 1/R + 1/R = 2/R

R1eq = R/2 = 0.5*R

when three resistors are in parallel, then

1/R2eq = 1/R + 1/R + 1/R = 3/R

R2eq = R/3 = 0.33*R

So we can see that If a third resistor is now connected in parallel with the original two, then equivalent resistance of the circuit decreases.

Explanation: 1. The third resistor gives yet another path for current to flow in the circuit, which means that the equivalent resistance is less.

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