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ICSE Class 10 Answered

combination of the resistor in parallel
Asked by aadrica.kanika | 27 Jul, 2019, 06:12: PM
answered-by-expert Expert Answer
 
Let us connect two resistors in parallel as shown in figure and connect the parallel combination to a battery that gives a potential difference V.
 
Let i1 and i2 be the currents passing through resistances R1 and R2 respectively.
 
If i is net current drawn from battery, then we have ,  i = i1 + i2   ...................(1)
 
if Req is the equivalent resistance, then we have,  Req = ( V / i )    or    i = ( V / Req )   .......................(2)
 
Since potential difference between points A and B is same as the potential difference between C and D,
 
we have ,  V = i1 × R1 = i2 × R2   ............................(3)
 
from eqn.(3), we get,   i1 = V/R1  and   i2 = V/R2  ...................(4)
 
using eqn.(1), (2) and (4), we get ,  (V / Req ) = ( V/R1 ) + ( V/R2 )    or   ( 1/ Req ) = (1/R1 ) +( 1/R2 )   .................(5)
 
Eqn.(5) gives the equivalent resistance of two resistors which are connected in parallel.
 
Eqn.(5) can be rewrittenas,  Req = (R1R2)/(R1+R2)
Answered by Thiyagarajan K | 27 Jul, 2019, 07:32: PM

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