Answer: The total resistance of resistors in series is equal to the sum of their individual resistances. That is, R  

total

​  

=R  

1

​  

+R  

2

​  

+R  

3

​  

.

The total resistance will always be less than the value of the SMALLEST resistance That is,  

R  

total

​  

1

​  

=  

R  

1

​  

1

​  

+  

R  

2

​  

1

​  

+  

R  

3

​  

1

​  

thatis,R=R  

total

​  

−1

.  

In this case, the total resistance of the resistors CONNECTED in series is given as R  

1

​  

+R  

2

​  

=45 - eqn 1

The total resistance of the resistors connected in parallel is given as  

R  

1

​  

1

​  

+  

R  

2

​  

1

​  

=  

10

1

​  

thatis,  

R  

1

​  

1

​  

+  

R  

2

​  

1

​  

=0.1 - eqn 2

Putting the value of R  

1

​  

+R  

2

​  

 in eqn 2, we get, R  

1

​  

R  

2

​  

=10×45=450ohms.

Now, From the identity, (R  

1

​  

−R  

2

​  

)  

2

=(R  

1

​  

+R  

2

​  

)  

2

−4R  

1

​  

R  

2

​  

,weget,R  

1

​  

−R  

2

​  

=15ohms - eqn 3.

Adding eqn 2 and eqn 3,  

2R  

1

​  

=60ohmsThatis,R  

1

​  

=30ohms.

Substituting this value in eqn 3, we get, R  

2

​  

=(30−15)=15ohms.

Hence, the values of the resistors are 30 OHMS and 15 ohms