Final answer:
The average voltage across the load in the transformer circuit with ideal diodes and a turns ratio of 7.1 is found by dividing the primary Vrms of 110V by 7.1 and then multiplying the secondary Vrms by 2/√π.
Step-by-step explanation:
To determine the average voltage (V) across the load in a transformer circuit, we begin by noting that the input is 110 Vrms (root mean square) at a frequency of 51 Hz. The transformer has a turns ratio of 7.1, which indicates the voltage is stepped down. With ideal diodes present in the circuit, the diodes will rectify the AC voltage into pulsating DC, for which the average voltage can be estimated using the Vrms of the secondary coil.
The first step is to calculate the output Vrms across the secondary. Since the transformer has a turns ratio of 7.1, this means for every 7.1 turns on the secondary coil, there is 1 turn on the primary coil. Therefore, to find the output Vrms, we calculate:
Secondary Vrms = Primary Vrms / Turns Ratio = 110 V / 7.1
Then, to find the average voltage of a full-wave rectified signal, we multiply the secondary Vrms by 2/√π (which is approximately 0.9).
Average Voltage = Secondary Vrms × (2/√π)
Note: The above solution assumes an ideal transformer and ideal diodes without considering any real-world inefficiencies such as diode voltage drops and transformer losses.