From Ohm's law -
V/I = R
V= IR
I = V/R
V/I = R
V= IR
I = V/R
RESISTANCE CONNECTIONS
1. SERIES CONNECTION
2. PARALLEL CONNECTION
SERIES CONNECTION-
From the upper diagram-
Here current I is same across all the resistances.
We know,
V = V1+V2+V3
IR = IR1 + IR2 + IR3 [from Ohm's law]
So, R = R1+ R2 +R3
PARALLEL CONNECTION-
From upper diagram-
Here V is same across all resistance,
We know,
I = I1 + I2 + I3
V/R = V/R1 + V/R2 + V/R3 [from Ohm's law]
So, 1/R = 1/R1 + 1/R2 + 1/R3
1/R = (R2R3 + R1R3 + R1R2)/(R1R2R3)
R = (R1R2R3)/(R2R3 + R1R3 + R1R2)
So, G = G1 + G2 + G3