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 can follow these steps:

### Step 1: Write down the expression for charge \( Q \)
The charge \( Q \) passing through a cross-section of the conductor is given by the equation:
\[ Q = 0.5 t^2 + t \quad \text{(in coulombs)} \]

### Step 2: Recall the definition of current
The current \( I \) is defined as the rate of change of charge with respect to time:
\[ I = \frac{dQ}{dt} \]

### Step 3: Differentiate the charge expression with respect to time
We need to differentiate \( Q \) with respect to \( t \):
\[ \frac{dQ}{dt} = \frac{d}{dt}(0.5 t^2 + t) \]
Using the power rule of differentiation:
\[ \frac{dQ}{dt} = 0.5 \cdot 2t + 1 = t + 1 \]

### Step 4: Substitute \( t = 1 \) into the current expression
Now we can find the current at \( t = 1 \) second:
\[ I = t + 1 \]
Substituting \( t = 1 \):
\[ I = 1 + 1 = 2 \, \text{A} \]

### Conclusion
The current through the conductor at \( t = 1 \) second is:
\[ \boxed{2 \, \text{A}} \]

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