Question

A step-down transformer has a 120 Vrms primary voltage applied. A 12 Vrms voltage is measured at the secondary. Assuming the transformer can be considered ideal, determine the turns ratio, n. If a 1  load is attached to the secondary of this transformer, what is the rms load current? What is the rms primary current?

Answer 1

Answer:

(a). The rms load current is 1.08 A.

(b). The rms primary current is 0.108 A.

Explanation:

Given that,

Primary voltage = 120

Secondary voltage = 12

Load = 10 ohm

We need to calculate the number of turns in primary and secondary coil

Using formula of voltage

$\dfrac{V_{1}}{V_{2}}=\dfrac{N_{1}}{N_{2}}$

Put the value into the formula

$\dfrac{N_{1}}{N_{2}}=\dfrac{120}{12}$

$\dfrac{N_{1}}{N_{2}}=10$

$\dfrac{N_{2}}{N_{1}}=0.1$

We need to calculate the resistance

Using formula of resistance

$R=10\times(\dfrac{N_{1}}{N_{2}})^2$

Put the value into the formula

$R=10\times(10)^2$

$R=1000\ \Omega$

We need to calculate the current in primary coil

Using formula of current

$I_{1}=\dfrac{120-12}{1000}$

$I_{1}=0.108\ A$

We need  to calculate the current in secondary coil

Using formula of current for secondary coil

$\dfrac{I_{1}}{I_{2}}=\dfrac{N_{2}}{N_{1}}$

$I_{2}=I_{1}\times\dfrac{N_{1}}{N_{2}}$

Put the value into the formula

$I_{2}=0.108\times10$

$I_{2}=1.08\ A$

Hence, (a). The rms load current is 1.08 A.

(b). The rms primary current is 0.108 A.