An alternating emf given by equation
`e=300sin(100pi)t V`
is applied to a resistance `100 Omega`. The rms current through the circuit is (in amperes).

Options

A. `3/sqrt(2)`
B. `9/sqrt(2)`
C. 3
D. `6/sqrt(2)`

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Identify the given parameters
The alternating emf is given by the equation:
\[ e = 300 \sin(100\pi t) \, \text{V} \]
From this equation, we can identify:
- The peak voltage \( E_0 = 300 \, \text{V} \)
- The angular frequency \( \omega = 100\pi \, \text{rad/s} \)

### Step 2: Calculate the RMS voltage
The RMS (Root Mean Square) voltage for an alternating current is given by the formula:
\[ E_{\text{rms}} = \frac{E_0}{\sqrt{2}} \]
Substituting the value of \( E_0 \):
\[ E_{\text{rms}} = \frac{300}{\sqrt{2}} \]

### Step 3: Calculate the RMS current
The RMS current \( I_{\text{rms}} \) through a resistor can be calculated using Ohm's law:
\[ I_{\text{rms}} = \frac{E_{\text{rms}}}{R} \]
Where \( R = 100 \, \Omega \) (the resistance given in the problem).
Substituting the value of \( E_{\text{rms}} \):
\[ I_{\text{rms}} = \frac{300/\sqrt{2}}{100} \]

### Step 4: Simplify the expression
Now, simplify the expression:
\[ I_{\text{rms}} = \frac{300}{100\sqrt{2}} = \frac{3}{\sqrt{2}} \, \text{A} \]

### Final Answer
Thus, the RMS current through the circuit is:
\[ I_{\text{rms}} = \frac{3}{\sqrt{2}} \, \text{A} \]