Question

Derive arelation for equivalent resistance when three resistors of resistance R1,R2,R3 are connected in parallel.3 mark answer please it's urgent​

Answer 1

Explanation:

Expert Verified

OT 1/Rp=1/R1 +1/R2+1/R3 Vi Thus, we may conclude that the reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances.

Answer 2

As we know that,

If the total current I,is equal to the sum of the separate current through each branch of the combination,then;

$\bold{I=I_1 + I_2 + I_3}$

Let R_p BD equivalent resistance of the parallel combination of resistors.By applying oham slaughter parallel combination of resistors, we have

$\bold \orange{I= \frac{V}{R_p}}$

On applying on slot to each resistor, we have

$\bold{I_1= \frac{V}{R_1}} \\ \\ \bold{ I_2= \frac{V}{R_2}} \\ \\ \bold{I_3= \frac{V}{R_3}}$

From all the above Equations

$\bold{\frac{V}{R_p} = \frac{V}{R_1} + \frac{V}{R_2} + \frac{V}{R_3}}\\ \\ or \\ \\ \bold\red{\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}}$

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