The amount of charge Q passed in time t through a cross-section of a wire is `Q=5t^(2)+3t+1`. The value of current at time t=5 s is

Options

A. 9A
B. 49A
C. 53A
D. None of these

Explanation

To find the current at time \( t = 5 \) seconds, we start with the given equation for charge \( Q \) passed through a cross-section of a wire:

\[ Q(t) = 5t^2 + 3t + 1 \]

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

\[ I(t) = \frac{dQ}{dt} \]

Now, we differentiate \( Q(t) \):

\[ \frac{dQ}{dt} = \frac{d}{dt}(5t^2 + 3t + 1) \]

Using the power rule of differentiation:

\[ \frac{dQ}{dt} = 10t + 3 \]

### Step 2: Substitute \( t = 5 \) seconds into the current equation.
Now, we need to find the value of current at \( t = 5 \) seconds:

\[ I(5) = 10(5) + 3 \]

Calculating this gives:

\[ I(5) = 50 + 3 = 53 \, \text{A} \]

### Final Answer:
The value of current at time \( t = 5 \) seconds is:

\[ \boxed{53 \, \text{A}} \]

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