If charge flown through a wire is given by `q=3sin(3t)`, then
Q. Find out the amount of charge flown through the wire at `t=((pi)/(6))` seconds.

Options

A. 3 coulombs
B. 6 coulombs
C. 1 coulomb
D. zero coulomb

Explanation

To find the amount of charge flown through the wire at \( t = \frac{\pi}{6} \) seconds, we start with the given equation for charge:

\[ q = 3 \sin(3t) \]

### Step 1: Substitute \( t \) into the equation
We need to substitute \( t = \frac{\pi}{6} \) into the equation:

\[ q = 3 \sin(3 \cdot \frac{\pi}{6}) \]

### Step 2: Simplify the argument of the sine function
Now, simplify the argument of the sine function:

\[ 3 \cdot \frac{\pi}{6} = \frac{3\pi}{6} = \frac{\pi}{2} \]

### Step 3: Evaluate the sine function
Next, we evaluate \( \sin\left(\frac{\pi}{2}\right) \):

\[ \sin\left(\frac{\pi}{2}\right) = 1 \]

### Step 4: Calculate the charge
Now, substitute this value back into the equation for \( q \):

\[ q = 3 \cdot 1 = 3 \, \text{coulombs} \]

### Final Answer
Thus, the amount of charge flown through the wire at \( t = \frac{\pi}{6} \) seconds is:

\[ \boxed{3 \, \text{coulombs}} \]

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