The rms value of an alternating current

Options

A. is equal to 0.707 times peak value
B. is equal to 0.636 times peak value
C. is equal sqrt2 times the peak value
D. none of the above

Explanation

To find the RMS (Root Mean Square) value of an alternating current, we can follow these steps:

### Step 1: Understand the Definition of RMS Value
The RMS value of an alternating current (AC) is defined as the effective value of the current that would produce the same amount of heat in a resistor as a direct current (DC) of the same value.

### Step 2: Know the Relationship Between Peak Value and RMS Value
The RMS value (I_RMS) is related to the peak value (I_0) of the current by the formula:
\[ I_{RMS} = \frac{I_0}{\sqrt{2}} \]

### Step 3: Calculate the RMS Value
Using the formula from Step 2:
\[ I_{RMS} = \frac{I_0}{\sqrt{2}} \]
We can also express this as:
\[ I_{RMS} = I_0 \times 0.707 \]
This shows that the RMS value is approximately 0.707 times the peak value.

### Step 4: Identify the Correct Option
Given the options:
- A) 0.707 times peak value
- B) 0.636 times peak value
- C) Square root of 2 times the peak value
- D) None of the above

From our calculation, we see that the correct answer is:
**Option A: 0.707 times peak value.**

### Final Answer
The RMS value of an alternating current is equal to 0.707 times the peak value.

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