Question

When three resistors are combined in parallel, the total resistance of the combination is __________.

less than any of the individual resistance values

the average of the individual resistance values

greater than any of the individual resistance values

Answer 1

When three resistors are connected in parallel, then total resistance of the combination is given by:

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

Req = (1/R1 + 1/R2 + 1/R3)^(-1)

Since the above value is not an average value of three resistance's value, As

R_avg = (R1 + R2 + R3)/3

Also Since a + b > (1/a + 1/b), So above sum cannot be greater than any of the individual values.

So value of total resistance of combination will be less than any of the individual resistance values

Also you can choose any three random value of resistor and verify this

Suppose: R1 = 1 ohm, R2 = 2 ohm, and R3 = 3 ohm

then, 1/Req = 1/1 + 1/2 + 1/3

Req = (1 + 1/2 + 1/3)^(-1) = (11/6)^(-1) = 6/11 = 0.5454 ohm

So Req is less than any of the individual resistance values

Correct option is A.