Question

in paralellel ,I=10a,V=5,R1=10,R2=?.
find R2 ​

Answer 1

Given :

In a parallel combination,

Current = 10A

Potential difference = 5 volts

R₁ = 10 ohms

To find :

The resistance of the 2nd resistor (R₂)

Solution :

firstly we have to find the resistance of the combination using ohm's law that is,

» At constant temperature the current flowing through a conductor is directly proportional to the potential difference across its ends.

V = RI

where,

• V denotes potential difference
• R denotes resistance
• I denotes current

substituting all the given values in the formula,

$\leadsto \sf V = RI$

$\leadsto \sf 5 = R(10)$

$\leadsto \sf R = \dfrac{5}{10}$

$\leadsto \sf R = \dfrac{1}{2} \: ohms$

In parallel combination,

» The reciprocal of the combined resistance of a number of resistance connected in parallel is equal to the sum of the reciprocal of all the individual resistances. .i.e.,

$\leadsto \sf{\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} }$

$\leadsto \sf{\dfrac{1}{ \dfrac{1}{2} } = \dfrac{1}{10} + \dfrac{1}{R_2} }$

$\leadsto \sf{2 = \dfrac{R_2 + 10}{10R_2} }$

$\leadsto \sf{20R_2= R_2 + 10 }$

$\leadsto \sf{20R_2 - R_2 = 10 }$

$\leadsto \sf{19R_2= 10 }$

$\leadsto \sf{ R_2 = \dfrac{10}{19} }$

$\leadsto \underline{\boxed{\sf{ R_2 = 0.52 \: ohms}}}$