To solve the problem, we will calculate the no-load current ($I_0$) of the transformer and determine its phase angle with respect to the voltage.

Given:

• Primary turns ($N_p$): $600$
• Secondary turns ($N_s$): $150$
• Secondary current ($I_s$): $60$ A
• Power factor of secondary ($\text{pf}_s$): $0.8$ (lagging)
• Primary current ($I_p$): $20$ A
• Power factor of primary ($\text{pf}_p$): $0.707$ (lagging)

We will use the following steps:

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Step 1: Transformer Current Relationship

Using the turns ratio, the ideal relationship between the primary and secondary currents is given by: $\frac{I_s}{I_p} = \frac{N_p}{N_s}$ Substitute the given values: $\frac{60}{I_p^\text{ideal}} = \frac{600}{150} \implies I_p^\text{ideal} = \frac{60 \times 150}{600} = 15 \text{ A}$ Thus, the ideal primary current ($I_p^\text{ideal}$) is $15 \, \text{A}$.

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Step 2: Magnetizing Component of Primary Current ($I_m$)

The actual primary current ($I_p = 20 \, \text{A}$) consists of two components:

1. The magnetizing (no-load) current ($I_0$).
2. The ideal current ($I_p^\text{ideal}$) that corresponds to the load current.

Using vector addition in the phasor domain: I_p = \sqrt{I_0^2 + I_p^\text{ideal}^2} Rearrange for $I_0$: I_0 = \sqrt{I_p^2 - I_p^\text{ideal}^2} Substitute values: $I_0 = \sqrt{20^2 - 15^2} = \sqrt{400 - 225} = \sqrt{175} = 13.23 \, \text{A}$

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Step 3: Phase Angle of $I_0$

The no-load current ($I_0$) lags the primary voltage. The phase angle of $I_0$ can be found using the power factor ($\text{pf}_p = 0.707$) of the primary: $\cos(\phi_p) = 0.707 \implies \phi_p = \cos^{-1}(0.707) = 45^\circ$

Thus, the no-load current ($I_0$) lags the voltage by $45^\circ$.

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Final Answer:

1. No-load current ($I_0$): $13.23 \, \text{A}$
2. Phase angle: $45^\circ$ lagging

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Do you want further clarification or a detailed explanation of any step?

Related Questions:

1. How is the ideal primary current ($I_p^\text{ideal}$) derived in transformers?
2. What does the power factor indicate about the phase relationship in AC systems?
3. Why is the no-load current significant in transformer operations?
4. How do transformer turn ratios affect primary and secondary currents?
5. What is the importance of phasor addition in analyzing AC circuits?

Tip:

Always ensure the primary and secondary power equations match when calculating transformer parameters, as energy conservation principles are critical!