An ac voltage is represented by
`E=220 sqrt(2) cos (50 pi) t`
How many times will the current become zero in 1 s?

Options

A. (A) 50 times
B. (B) 100 times
C. (C) 30 times
D. (D) 25 times

Explanation

To solve the problem, we need to determine how many times the current becomes zero in one second, given the AC voltage equation:

\[ E = 220 \sqrt{2} \cos(50 \pi t) \]

### Step 1: Identify the angular frequency (ω)
The equation is in the form of \( E = E_0 \cos(\omega t) \), where \( \omega \) is the angular frequency. From the given equation, we can see that:

\[ \omega = 50 \pi \]

### Step 2: Calculate the frequency (f)
The angular frequency \( \omega \) is related to the frequency \( f \) by the formula:

\[ \omega = 2 \pi f \]

Substituting the value of \( \omega \):

\[ 50 \pi = 2 \pi f \]

### Step 3: Solve for frequency (f)
We can divide both sides by \( 2 \pi \):

\[ f = \frac{50 \pi}{2 \pi} = 25 \, \text{Hz} \]

### Step 4: Determine the number of cycles in one second
The frequency \( f \) indicates the number of cycles per second. Since \( f = 25 \, \text{Hz} \), this means there are 25 cycles in one second.

### Step 5: Calculate how many times the current becomes zero
In each cycle of an AC waveform, the current becomes zero twice (once when it goes from positive to negative and once when it goes from negative to positive). Therefore, in 25 cycles, the current will become zero:

\[ \text{Total zeros in 1 second} = 25 \, \text{cycles} \times 2 \, \text{zeros/cycle} = 50 \]

### Conclusion
Thus, the current will become zero 50 times in one second.

### Final Answer
The current becomes zero **50 times** in 1 second.

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