Question

derive an expression for equivalent resistance in a combination of 3 resistors r1,r2,r3 in. 1)parellel,2)series.

Answer 1

Hello your answer





take three resistors R1 R2 R3 connected in parallel and connect a battery of V volts in this case the P,d across the ends will be the same the current flowing is not same......

Total I=11+12------------------(1)
from ohm's law
I=V/r-----------------------------------(2)
I1=V/r1-------------------(3)
12=V/r2-----------------(4)
13=V/r3------------------(5)




putting the value of 11 12 and 13 in 1

V/r=v/r1+v/r2+v/r3
=v/r=v[1/R1+1/R2+1/r3]
=1/r=1/r1/R2+1/r3



For series

1)total potential difference across a combination of resistors in series is equal to the sum of potential difference across the individual resistor.
V=V1+V2+V3
let I be the current in the circuit.the current through each resistor is also I.it is possible to replace the three resistors joined in series by an equivalent resistor of resistance R.applying Ohm's law.
V=IR
on applying Ohm's law to the three resistor respectively we father have
V1=IR1
V2=IR2
V3=IR3

but

V=V1+V2+V3
IR=IR1+IR2+IR3
ii) power rating of electric iron =1kw=1000W
V=220V
P=VI


I=P/V=1000/220 4.54A2

Hence a fuse of rating 5A can be used because it can wear the current



Thanks!!!