An AC voltage of `V=220sqrt2 sin (100pit+(pi)/(2))V` is applied across a DC votlmeter, its reading will be

Options

A. `220sqrt2V`
B. 110V
C. 220V
D. zero

Answer

To find the reading of a DC voltmeter when an AC voltage is applied, we can follow these steps:

### Step 1: Identify the given AC voltage
The AC voltage is given as:
\[ V = 220\sqrt{2} \sin(100\pi t + \frac{\pi}{2}) \]

### Step 2: Understand the function of a DC voltmeter
A DC voltmeter measures the average value of the voltage over a complete cycle. For an AC voltage expressed as a sine function, the average value over one complete cycle is important.

### Step 3: Analyze the sine function
The sine function, \(\sin(\theta)\), oscillates between -1 and 1. Therefore, the average value of \(\sin(\theta)\) over one complete cycle (from 0 to \(2\pi\)) is:
\[ \text{Average value of } \sin(\theta) = 0 \]

### Step 4: Calculate the average value of the AC voltage
Since the average value of \(\sin(100\pi t + \frac{\pi}{2})\) over one complete cycle is 0, we can conclude that:
\[ \text{Average value of } V = 220\sqrt{2} \times 0 = 0 \]

### Step 5: Conclusion
The reading of the DC voltmeter, which measures the average value of the applied AC voltage, will be:
\[ \text{Reading of the voltmeter} = 0 \, \text{V} \]

Thus, the final answer is:
\[ \text{The reading of the DC voltmeter will be } 0 \, \text{V}. \]

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