(i) Three resistances R1,R2 and R3 are connected in parallel to one another between the same two points. In this case, the potential difference across the ends of all the resistance will be the same.
∴‌‌V=V1=V2=V3...(i)
If the total current flowing through the circuit is I, then the current passing through R1 will be I1 through R2 will be I2 and through R3 will be I3.Then
I=I1+I2+I3...(ii)
If R is the effective resistance of the circuit, connected across a battery of V volts, through which I current flows, then
I=‌

V

R

Substituting the values in eq. (ii), we get
⇒‌

V

R

=‌

V

R1

+‌

V

R2

+‌

V

R3

⇒‌

V

R

=V[‌

1

R1

+‌

1

R2

+‌

1

R3

]
⇒‌

1

R

=‌

1

R1

+‌

1

R2

+‌

1

R3

(ii) Given: R1=4Ω,R2=4Ω,R3=8Ω Let, resultant resistance between a and c be R′
Then, ‌‌R′=R1+R2
(Series combination)
R′=4+4=8Ω
If R is the effective resistance between A and B, then
‌

1

R

=‌

1

R′

+‌

1

R3

( R′ and R3 are in parallel combination)
‌‌

1

R

‌=‌

1

8

+‌

1

8

=‌

2

8

⇒‌R‌=4Ω