Derive the formula for equivalent resistance of the resistor arranged

1.	Derive the formula for equivalent resistance of the resistor arranged in parallel combination
Answer» LET I1,I2,I3 be the current flowing through R1,R2,R3 respectively therefore, I=I1+I2+I3_____________(i) let the effective resistance of this parallel combination be Rp, then using, OHM's law I=V/Rp_______________________(II) As V is same for all resistor, therefore I1=V/R1 ,I2=V/R2 ,I3=V/R3_________(iii) hence, from eqn (i), (ii),(ii), we get V/Rp=V/P1+V/R2+V/R3+V[ 1/R1+1/R2+1/R3] \|____________________ \| \| 1/R1 + 1/R2+ 1/R3 \| \|____________________\|

Derive the formula for equivalent resistance of the resistor arranged in parallel combination

Answer»

LET I1,I2,I3 be the current flowing through R1,R2,R3 respectively

therefore, I=I1+I2+I3_____________(i)

let the effective resistance of this parallel combination be Rp, then using, OHM's law

I=V/Rp_______________________(II)

As V is same for all resistor, therefore

I1=V/R1 ,I2=V/R2 ,I3=V/R3_________(iii)

hence, from eqn (i), (ii),(ii), we get

V/Rp=V/P1+V/R2+V/R3+V[ 1/R1+1/R2+1/R3]

|____________________ |

| 1/R1 + 1/R2+ 1/R3 |

|____________________|

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Derive the formula for equivalent resistance of the resistor arranged in parallel combination

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