Question

find the parallel resistance to be connected to a 300 ohm resistance such that the current passing through the 300 ohms resistance should be 10 percentage initial value

Answer 1

Let a resistor of resistance R is connected in parallel with 300 Ω resistor.
Let intial Curren passing through it is i.

Case 1 :- when i current passing through only resistance 300Ω .
From Ohm's law, V = 300i

Case 2 :- now, R is connected with 300Ω resistor.
so, potential difference across each resistor will be same.
e.g., potential difference across 300 Ω = V and potential difference actoss R = V
so, we can say i₁ × R₁ = i₂ × R₂
A/C to question,
Current passing through 300Ω is 10 % of i = 0.1i
So, i₁ = 0.1i , R₁ = 300Ω , i₂ = i - 0.1i = 0.9i and R₂ = R
∴ 0.1i × 300 = 0.9 × R
⇒ 300 = 9R
⇒R = 300/9 = 100/3 Ω

Answer 2

Let us try to make the solution to the question simpler,
Let us assume this resistance is connected to a 300V power supply,
So,
Current through resistor= (300/300)
                                       =1 A
Now,
only 10% should flow through 300 ohm resistor
So, 0.1A should flow through 300 ohm resistor
So,
other 0.9  A will flow though the other resistor,
Now potential in parallel is always the same,so
V1 = V2
0.1 × 300 = 0.9 × R
R= 300/9
R= 100/3 ohm
So, a resistor of 100/3 ohm should be connected