Question

The resistances of the primary and secondary coils of a transformer are 76 and 13 Ohms, respectively. Both coils are made from lengths of the same copper wire. The circular turns of each coil have the same diameter. Find the turns ratio Ns/Np.

Answer 1

Answer:

Ns/Np = 0.171

Explanation:

First, we will find the ratio of lengths of each wire:

$R_{p} = \frac{\rho L_{p}}{A}\\\\R_{s} = \frac{\rho L_{s}}{A}$

where,

Rs = Resistance of secondary coil

Rp = Resistance of Primary Coil

ρ = resistivity of copper

Ls = Length of the secondary coil

Lp = Length of theprimary coil

A = Area of cross-section of wie

Since the material and wire are the same. Therefore, dividing both equations, we get:

$\frac{R_{s}}{R_{p}} = \frac{L_{s}}{L_{p}} \\\\\frac{L_{s}}{L_{p}} = \frac{13}{76}\\\\\frac{L_{s}}{L_{p}} = 0.171$

The number of turns are given as:

$N_{s} = \pi DL_{s}\\N_{p} = \pi DL_{p}$

where,

Ns = No. of turns in the secondary coil

Np = No. of turns in the primary coil

D = Diameter of circular turns

D is the same for both coils. Therefore, dividing both equaions:

$\frac{N_{s}}{N_{p}} = \frac{L_{s}}{L_{p}}$

Ns/Np = 0.171