Three wires of resistance r1 , r2 and r3 having length in ratio 2:3:4 and diameter in ratio 3:4:5 forming parallel combination .5A of current is distributed among the three resistors. Find the current in each resistor
Answers
The currents are in the ratio of 54:64:75
Explanation :
Given diameter of he wires in the ratio of 3:4:5
=> Area will be in ratio of 9:16:25
Also length are in the ratio of 2 : 3:4
since resistance of a wire is given by,
R = ρL/A
hence their resistance will be in the ratio of 2/9 : 3/16 : 4/25
In parallel combination the net resistance is given by,
1/R = 1/r₁ + 1/r₂ + 1/r₃
=> 1/R = 9/2 + 16/3 + 25/4
=> 1/R = (54+64+75)/12 = 193/12
=> R = 12/193
Hence net voltage across the circuit,
V = IR = 5 x 12/193 = 60/193
Since voltage across each element in a parallel circuit is equal,
Hence
I₁ = V/r₁ = (60/193)/(2/9) = 270/193
I₂ = V/r₂ = (60/193)/(3/16) = 320/193
I₃ = V/r₃ = (60/193)/(4/25) = 375/193
Hence the currents are in the ratio of
I₁ : I₂ : I₃ = 270 : 320 : 375 = 54:64:75