Dimensions of charge are

Options

A. `M^(0)L^(0)T^(-1)A^(-1)`
B. `MLTA^(-1)`
C. `T^(-1)A`
D. `TA`

Answer

To find the dimensions of charge, we can use the relationship between charge (Q), current (I), and time (T). Here’s a step-by-step solution:

### Step 1: Understand the relationship between charge, current, and time.
The fundamental relationship we need is given by the formula:
\[ I = \frac{Q}{T} \]
where:
- \( I \) is the current,
- \( Q \) is the charge,
- \( T \) is the time.

### Step 2: Rearrange the formula to express charge in terms of current and time.
From the formula, we can rearrange it to find charge:
\[ Q = I \times T \]

### Step 3: Identify the dimensions of current and time.
- The dimension of current (I) is represented as \([I] = [A]\) (where A stands for Ampere).
- The dimension of time (T) is represented as \([T] = [T]\).

### Step 4: Substitute the dimensions into the equation for charge.
Now, substituting the dimensions of current and time into the equation for charge:
\[ [Q] = [I] \times [T] = [A] \times [T] \]

### Step 5: Write the final expression for the dimensions of charge.
Thus, the dimensions of charge can be expressed as:
\[ [Q] = [A][T] \]

### Conclusion:
The dimensions of charge are \([A][T]\).

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