Question

Show how you would connect three resistors, each of resistance 6 ohm, so that the combination has a resistance of (i) 9 ohm (ii) 4 ohm

Answer 1

Answer:

To obtain a combined resistance of 9 ohms, three resistors each of resistance 6 ohm should be connected in a parallel circuit and one in series.  

In a parallel circuit, the equivalent resistance of all the resistors connected is equal to the reciprocal value of the sum of the individual resistances.

In a series circuit, the equivalent resistance of all the resistors connected is equal to the sum of the resistance values of each of the individual resistor.

So in a parallel circuit, total resistance =   or  

R t= .  

In a series circuit, total resistance  = R1 +R2 + R3

(i) To get 9 ohms, two resistors should be connected in parallel and one in series.

So,

Rt in parallel will be  

Rt =

= 3 ohms

One resistor is connected in series with the 3 ohms, so  

Rt in series will be Rt = R1 +R2 = 6+3 = 9 ohms

(ii) To obtain a combined resistance of 4 ohms, two resistors (of 6 ohms each) are connected in series and one in parallel to the series.

So,

Rt in series = R1 +R2 = 6+6 = 12 ohms

Rt in parallel = = 4 Ohms