A mixer of `100 Omega` resistance is connected to an `A.C` source of `200 V` and `50 "cycles"//"Sec"`. The value of average potentail difference across the mixer will be

Options

A. `308 V`
B. `264 V`
C. `220 V`
D. zero

Explanation

To find the average potential difference across the mixer connected to an AC source, we can follow these steps:

### Step 1: Understand the AC Voltage
The AC voltage can be represented as:
\[ V(t) = V_0 \sin(\omega t) \]
where:
- \( V_0 \) is the peak voltage,
- \( \omega \) is the angular frequency.

### Step 2: Determine the RMS Voltage
Given that the RMS voltage \( V_{rms} \) is 200 V, we can find the peak voltage \( V_0 \) using the relationship:
\[ V_0 = V_{rms} \times \sqrt{2} \]
Substituting the given value:
\[ V_0 = 200 \times \sqrt{2} \]

### Step 3: Calculate the Angular Frequency
The angular frequency \( \omega \) is calculated as:
\[ \omega = 2\pi f \]
where \( f \) is the frequency. Given \( f = 50 \) cycles/second:
\[ \omega = 2\pi \times 50 \]

### Step 4: Analyze the Average Value of AC Voltage
The average value of a sinusoidal AC voltage over one complete cycle is zero. This is because the positive half of the cycle cancels out the negative half. Therefore, the average potential difference across the mixer is:
\[ V_{avg} = 0 \]

### Final Answer
Thus, the value of the average potential difference across the mixer is:
\[ \text{Average Potential Difference} = 0 \, \text{V} \]

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