Question 29: AC fundamentals

Question

In the $$\mathrm{A} . \mathrm{C}$$. circuit given below, voltmeters $$\mathrm{V}_1$$ and $$\mathrm{V}_2$$ read $$100 \mathrm{~V}$$ each. Find the reading of the voltmeter $$\mathrm{V}_3$$ and the ammeter $$\mathrm{A}$$.

Accepted Answer

To solve this problem, we can use the principles of an ideal transformer along with OhmÃ¢ÂÂs law. HereÃ¢ÂÂs the step-by-step process:
Determine the Voltage Ratio:
An ideal transformer follows the relationship:
$$\frac{V_s}{V_p} = \frac{N_s}{N_p}$$
Given:
Number of primary turns, $$N_p = 400$$
Number of secondary turns, $$N_s = 800$$
Primary voltage, $$V_p = 20\, 	ext{V}$$
Compute the secondary voltage:
$$V_s = V_p 	imes \frac{N_s}{N_p} = 20\, 	ext{V} 	imes \frac{800}{400} = 20\, 	ext{V} 	imes 2 = 40\, 	ext{V}$$
Calculate the Secondary Current:
With the load resistance on the secondary being 4 ohms, use Ohm's law:
$$I_s = \frac{V_s}{R} = \frac{40\, 	ext{V}}{4\, \Omega} = 10\, 	ext{A}$$
Find the Primary Current Using Power Conservation:
For an ideal transformer, power is conserved (ignoring losses):
$$V_p 	imes I_p = V_s 	imes I_s$$
Solve for the primary current ($$I_p$$):
$$I_p = \frac{V_s 	imes I_s}{V_p} = \frac{40\, 	ext{V} 	imes 10\, 	ext{A}}{20\, 	ext{V}} = \frac{400}{20} = 20\, 	ext{A}$$
Thus, the primary current is 20 A, which corresponds to Option B.

Answer

220 V, 2 A

Answer

110 V, 2 A

Answer

110 V, 4 A

Answer

220 V, 1 A

AC fundamentals

In the $\mathrm{A} . \mathrm{C}. circuit given below, voltmeters \mathrm{V}_1 and \mathrm{V}_2 read 100 \mathrm{~V} each. Find the reading of the voltmeter \mathrm{V}_3 and the ammeter \mathrm{A}$.

Choose the correct answer: