Question

find equivalent resistance if three resistances are joined in series and parallel combination with two examples

Answer 1

Heya.....!!!

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PARALLEL COMBINATION :-

Consider 3 resistors in parallel ( R1 ,R2 and R3 . )

Total current ( I )

• Current in 3 branches = I1 , I2 and I3
• Total voltage = V

=> I = I1 + I2 + I3

=> I1 = V / R1
=> I2 = V /R2
=> I3 = V / R3

I1 + I2 + I3 = V / R1 + V / R2 + V / R3

Let equivalent resistance be ( Re )

=> Re = V / I => I = V / Re

=> V / Re = V/ R1 + V / R2 + V / R3

♦ => 1 / Re = 1 / R1 + 1 / R2 + 1 / R3

=> In parallel combination the equivalent resistance is the sum of reciprocal of the individual resistance

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SERIES COMBINATION:-



Consider 3 resistors , R1 , R2 and R3 connected in series .

By Ohm' Law the potential drop across each resistor is given by :-

=> V1 = IR1
=> V2 = IR2
=> V3 = IR3

Let total potential be ( V )

V = V1 + V2 + V3

V = IRe ( Re is the equivalent resistance . )

Thus ,,

•• IRe = IR1 + IR2 + IR3

♦ Re = R1 + R2 + R3 .

we can say that equivalent resistance in series combination is the individual sum of resistance .

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Answer 2

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PARALLEL COMBINATION :-

Consider 3 resistors in parallel ( R1 ,R2 and R3 . )

Total current ( I )

• Current in 3 branches = I1 , I2 and I3

• Total voltage = V

=> I = I1 + I2 + I3

=> I1 = V / R1

=> I2 = V /R2

=> I3 = V / R3

I1 + I2 + I3 = V / R1 + V / R2 + V / R3

Let equivalent resistance be ( Re )

=> Re = V / I => I = V / Re

=> V / Re = V/ R1 + V / R2 + V / R3

♦ => 1 / Re = 1 / R1 + 1 / R2 + 1 / R3

=> In parallel combination the equivalent resistance is the sum of reciprocal of the individual resistance

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SERIES COMBINATION:-

Consider 3 resistors , R1 , R2 and R3 connected in series .

By Ohm' Law the potential drop across each resistor is given by :-

=> V1 = IR1

=> V2 = IR2

=> V3 = IR3

Let total potential be ( V )

V = V1 + V2 + V3

V = IRe ( Re is the equivalent resistance . )

Thus ,,

•• IRe = IR1 + IR2 + IR3

♦ Re = R1 + R2 + R3 .

we can say that equivalent resistance in series combination is the individual sum of resistance .

HOPE SO IT WILL HELP.....