An alternating voltage completes 80 cycles in 2 seconds. Find the frequency.
40 Hz
Calculating Alternating Voltage Frequency
The frequency of an alternating voltage tells us how many complete cycles of the voltage waveform occur in one second. It is typically measured in Hertz (Hz).
Understanding Frequency
Frequency is defined as the ratio of the number of cycles completed to the time taken to complete those cycles.
Mathematically, the formula for frequency is:
$$\text{Frequency} (f) = \frac{\text{Number of Cycles}}{\text{Time Taken} (t)}$$
Applying the Data
In this problem, we are given:
- Number of cycles = 80 cycles
- Time taken = 2 seconds
Performing the Calculation
Using the formula for frequency:
$$f = \frac{80 \text{ cycles}}{2 \text{ seconds}}$$
$$f = 40 \text{ cycles/second}$$
Since 1 cycle/second is equal to 1 Hertz (Hz), the frequency is:
$$f = 40 \text{ Hz}$$
Result Summary
The calculated frequency of the alternating voltage is 40 Hz.
| Quantity | Value |
|---|---|
| Number of Cycles | 80 |
| Time Taken | 2 seconds |
| Frequency (Calculated) | 40 Hz |
This means the alternating voltage completes 40 cycles every second.
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