Question

Derive an expression for equivalent resistance when two resistors R1 and R2 are connected in parallel

Answer 1

• In  parallel connections, it is observed that the total current I, is equal to the sum of the separate currents through each branch of the combination.  ie., total I = I1 + I2 + I3

• Let Rp be the equivalent resistance of the parallel combination of resistors.

• By applying Ohm's law to the parallel combination of resistors, we have  

I = V/Rp  (Equation 1)

• On applying Ohm's law to each resistor, we have                                          I1 =   V/R1 ; I2 = V/R2; and I3 + V/R3     (Equation 2)

• From  eqns.1 and2 we have                                                                                     V/Rp = V/R1 + V/R2 + V/R3                                                                                or 1/Rp =  1/R1 + 1/R2 +  1/R3

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 individuals resistances.

HPOE U GOT THE ANS.

PLS MARK AS BRAINLIEST IF IT HELPED.

Answer 2

Explanation:

• In parallel combination of resistor, electric current through each and every resistor divides while the voltage across each resistor remains the same.
• The electric current through each resistor is given by :

$I_1=\dfrac{V}{R_1}\\\\I_2=\dfrac{V}{R_2}$

• Let the equivalent resistance is given by :

$I=\dfrac{V}{R_p}$

• Total current through the circuit is given by :

$I=I_1+I_2\\\\\dfrac{V}{R_p}=\dfrac{V}{R_1}+\dfrac{V}{R_2}\\\\\dfrac{1}{R_p}=\dfrac{1}{R_1}+\dfrac{1}{R_2}$

So, the above formula is the required formula for equivalent resistance of resistors.

Learn more,

Equivalent combination

https://brainly.in/question/375541