Question

What different resistances can be obtained by using two 2.0-Ω resistors and one 4.0-Ω resistor? You must use all three of them in each possible combination.

Answer 1

here,

case 1)

when all are in series

the equivalent resistance ,Req = 2 ohm + 2 ohm + 4 ohm = 8 ohm

case 2)

when all are in parallel

the equivalent resistance be Req

1/Req = 1/2 + 1/2 + 1/4

Req = 0.8 ohm

case 3)

when two 2 ohms are in prallel and 4 ohm is in series with them

when two 2 ohms are in prallel their equivalent resistance , R1 = 2/2 = 1 ohm

R1 and 4 ohm is in series , the equivalent resistance , Req = R1 + 4 ohm

Req = 5 ohm

case 4)

when one 2 ohm and 4 ohm are in prallel and one 2 ohm is in series with them

when 2 ohm and 4 ohm are in prallel their equivalent resistance , R1 = 2 * 4 /(2 + 4) = 1.33 ohm

R1 and 2 ohm is in series , the equivalent resistance , Req = R1 + 2 ohm

Req = 3.33 ohm

case 5)

when two 2 ohms are in series and 4 ohm is in parallel with them

when 2 ohm and 2 ohm are in series , their equivalent resistance , R1 = 2 ohm + 2 ohm = 4 ohm

when R1 and 4 ohm are in parallel , their equivalent resistance , Req = R1 * 4 /(R1 + 4)

Req = 4 * 4 /(4 + 4) = 2 ohm

case 6)

when 2 ohm and 4 ohm are in series and one 2 ohm is in parallel with them

when 2 ohm and 4 ohm are in series , their equivalent resistance , R1 = 2 ohm + 4 ohm = 6 ohm

when R1 and 2 ohm are in parallel , their equivalent resistance , Req = R1 * 2 /(R1 + 2)

Req = 6 * 2 /(6 + 2) = 1.5 ohm