Question

Deduce the expression for the equivalent resistance of the parallel combination of three resistors R1,R2 and R3. Consider the following electric circuit:

(i) Which two resistors are connected in series?
(ii) Which two resistors are connected in parallel?
(iii) If every resistor of the circuit is of 2 ohm. what current will flow in the circuit?

Answer 1

hey mate your answer is ....

■1■

for series connection ..

we know in series VOLTAGE or POTENTIAL DIFFERENCE is different along the resistor and CURRENT is same ...

so ..

Vs= V1 + V2 + V3 ...[1]

we know ... V= IR {by ohms law}

Vp = IRs

v1 = ir1

v2 = ir2

v3 = ir3

by putting value in [1]

IR s = ir1 + ir2 + ir3

IRs = i (r1+r2 +r3)

Rs = R1 + R2 + R3 ........ {first ans}

■2■

for parallel connection ...

we know in parallel connection VOLTAGE is same but CURRENT is different

so ..

Ip = I1 + I2 + I3 ....... [2]

v = ir {by ohm law }

v/r = i

ip = v / rp

i1 = v/ r1

i2 = v/ r2

i3 = v/ r3

putting value in [2]

v/rp = v/r1 + v/r2 + v/r3

v / rp = v( 1/r1 + 1/r2 +1/r3)

1/rp = 1/r1 + 1/r2 +1/r3 ... {2nd ans}