Derive the equivalent resistance when resistors are connected in (i) series (ii) parallel. ( Draw diagram to support your answer)
Answers
In series connection
When resistors are connected in series the potential difference gets divided
V = V1 + V2....... equation 1
The current through each resistor in series will be the same
According to Ohm's law
V =IR
So,
in our case
V1 = I * R1 ... equation 2
V2= I * R2... equation 3
equation 1 can be weitten as
I*R= V1 + V2
substituting eq 2 and eq3
IR = I * R1 + I * R2
IR = I ( R1 + R2 )
I can be cancelled ( when I in the left side of equation comes to right side it takes the division form and hence gets cancelled)
therefore
R = R1 + R2
In parallel connection
The total current is the sum of the current through all branch circuits in parallel connection
I = I1 + I2
since R is the effective resistance
By ohm's law
V/R = V/R1 + V/R2 ( potential difference through each resistor is same in parallel connection)
V(1/R) = V ( 1/R1 + 1/R2 )
V gets cancelled
so
1/R = 1/R1 + 1/R2
cross multiply,
1/R = (R1 + R2) / R1 * R2
R = (R1 * R2)/R1 + R2
if resistors are of same value then ,
R = r/n
where n is the no.of resistors and r is the resistance of one resistor
