Question

A transformer has 650 primary turns and 15 secondary turns. (a) If Vₚ is 120 V(rms), what is Vs with an open circuit? If the secondary now has a resistive load of 13Ω, what is the current in the (b) primary and (c) secondary?

Answer 1

The open-circuit secondary voltage (Vs) of a transformer is found using the turns ratio formula and is calculated to be 2.77 V (rms). The primary current (Ip) can be found by using the conservation of power principle and Ohm's Law, after determining the secondary current (Is), which itself is determined again using Ohm's Law to be 0.213 A (rms).

Step-by-step explanation:

The question is related to the operation of a transformer, which is a device in physics that transfers electrical energy between two circuits through electromagnetic induction. Specifically, we are dealing with a step-down transformer since the number of primary turns exceeds the number of secondary turns. Now, let's find the answers to the given problems:

(a) Open Circuit Secondary Voltage (Vs)

The open-circuit secondary voltage can be determined using the formula for transformer action, which relates the voltage across the primary (Vp) to the voltage across the secondary (Vs) through the number of turns in the primary (Np) and the secondary (Ns):
Vs = Vp × (Ns / Np)

Substituting the given values:

Vs = 120 V × (15 / 650) = 2.77 V (rms)

(b) Primary Current (Ip)

To find the primary current, we use the conservation of power principle in ideal transformers which states that the power in the primary coil (Pp) equals the power in the secondary coil (Ps), assuming no losses:

Pp = Ps

Knowing the secondary resistance (Rs) and using Ohm's law, we find that Is = Vs / Rs. With this, we can calculate the power in the secondary:

Ps = Is²Rs

And since Pp = Ps, we have:

Ip = Ps / Vp

Thus, after finding Is, we can determine Ip.

(c) Secondary Current (Is)

With the secondary voltage (Vs) already known, we can calculate the secondary current using Ohm's law

Is = Vs / Rs = 2.77 V / 13 Ω = 0.213 A (rms)