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 will follow these steps:

### Step 1: Write down the equation for charge
The charge \( q \) flowing through the wire is given by the equation:
\[ q = 3 \sin(3t) \]

### Step 2: Substitute the value of \( t \)
We need to find the charge at \( t = \frac{\pi}{6} \). Substitute this value into the equation:
\[ q = 3 \sin(3 \cdot \frac{\pi}{6}) \]

### Step 3: Simplify the argument of the sine function
Calculate \( 3 \cdot \frac{\pi}{6} \):
\[ 3 \cdot \frac{\pi}{6} = \frac{3\pi}{6} = \frac{\pi}{2} \]
Now substitute this back into the equation:
\[ q = 3 \sin\left(\frac{\pi}{2}\right) \]

### Step 4: Evaluate the sine function
The value of \( \sin\left(\frac{\pi}{2}\right) \) is known to be 1. Therefore:
\[ q = 3 \cdot 1 = 3 \]

### Step 5: Write the final answer
Thus, the amount of charge flown through the wire at \( t = \frac{\pi}{6} \) seconds is:
\[ q = 3 \text{ Coulombs} \]

### Summary
The charge flown through the wire at \( t = \frac{\pi}{6} \) seconds is 3 Coulombs.

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