Charge Q passing through a cross-section of conductor at an instant is given by `Q= ( 0.5 t^(2) + t) C ` where t is in second . Current through the conductor at `t=1` is

Options

A. Zero
B. 1A
C. 2A
D. `-1A`

Answer

To find the current through the conductor at \( t = 1 \) second, we start with the given expression for charge \( Q \):

\[ Q = 0.5 t^2 + t \quad \text{(in coulombs)} \]

### Step 1: Differentiate the charge with respect to time
The current \( I \) is defined as the rate of change of charge with respect to time, which can be expressed mathematically as:

\[ I = \frac{dQ}{dt} \]

Now, we need to differentiate \( Q \) with respect to \( t \):

\[ \frac{dQ}{dt} = \frac{d}{dt}(0.5 t^2 + t) \]

### Step 2: Apply the differentiation rules
Using the power rule of differentiation, we differentiate each term:

1. The derivative of \( 0.5 t^2 \) is \( 0.5 \cdot 2t = t \).
2. The derivative of \( t \) is \( 1 \).

Thus, we have:

\[ \frac{dQ}{dt} = t + 1 \]

### Step 3: Substitute \( t = 1 \) into the current equation
Now we substitute \( t = 1 \) into the expression for current:

\[ I = t + 1 = 1 + 1 = 2 \, \text{A} \]

### Conclusion
The current through the conductor at \( t = 1 \) second is:

\[ \boxed{2 \, \text{A}} \]