A large transformer operating at no-load draws an exciting current $I_{ o }$ of 5 A when the primary is connected to a 120 V, 60 Hz source (Fig. 2a). From a wattmeter test it is known that the iron losses are equal to 180 W.

Calculate
a. The reactive power absorbed by the core
b. The value of $R_{ m } \text { and } X_{ m }$

c. The value of $I_{ f }, I_{ m }, \text { and } I_{ o }$

Question

A large transformer operating at no-load draws an exciting current [latex]I_{ o }[/latex] of 5 A when the primary is connected to a 120 V, 60 Hz source (Fig. 2a). From a wattmeter test it is known that the iron losses are equal to 180 W.

Calculate
a. The reactive power absorbed by the core
b. The value of [latex]R_{ m } ext { and } X_{ m }[/latex]

c. The value of [latex]I_{ f }, I_{ m }, ext { and } I_{ o }[/latex]

Accepted Answer

a. The apparent power supplied to the core is

[latex]\begin{aligned}S_{ m } &=E_{1} I_{ o }=120 imes 5 \&=600 VA\end{aligned}[/latex]

The iron losses are

[latex]P_{ m }=180 W[/latex]

The reactive power absorbed by the core is

[latex]\begin{aligned}Q_{ m } &=\sqrt{S_{ m }^{2}-P_{ m }^{2}}=\sqrt{600^{2}-180^{2}} \&=572 var\end{aligned}[/latex]

b. The impedance corresponding to the iron losses is

[latex]\begin{aligned}R_{ m } &=E_{1}^{2} / P_{ m }=120^{2} / 180 \&=80 \Omega\end{aligned}[/latex]

The magnetizing reactance is

[latex]\begin{aligned}X_{ m } &=E_{1}^{2} / Q_{ m }=120^{2} / 572 \&=25.2 \Omega\end{aligned}[/latex]

c. The current needed to supply the iron losses is

[latex]\begin{aligned}I_{ f } &=E_{1} / R _{ m }=120 / 80 \&=1.5 A\end{aligned}[/latex]

The magnetizing current is

[latex]\begin{aligned}I_{ m } &=E_{1} / X_{ m }=120 / 25.2 \&=4.8 A\end{aligned}[/latex]

The exciting current [latex]I_{ o }[/latex] is

[latex]\begin{aligned}I_{ o } &=\sqrt{I_{ f }^{2}+I_{ m }^{2}}=\sqrt{1.5^{2}+4.8^{2}} \&=5 A\end{aligned}[/latex]

The phasor diagram is given in Fig. 2b.

Question 10.1: A large transformer operating at no-load draws an exciting c...

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