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.**

**Let me know if you've any query.**

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