Question

A current of \(2\,\text{A}\) flows through a resistor for \(10\) minutes. What is the total charge that passes through the resistor?

• A. \(600\,\text{C}\)
• B. \(1200\,\text{C}\)
• C. \(200\,\text{C}\)
• D. \(2400\,\text{C}\) \bigskip

Hint:

Current in amperes already means coulombs flowing per second, so total charge equals current multiplied by time in seconds. You can also work entirely in minutes by first converting the current into coulombs per minute.

Answer 1

The Correct Option is B

Concept: Electric current is defined as the rate of flow of electric charge. The relation between charge, current, and time is given by: \[ Q = It \] where \begin{itemize} \item \(Q\) = total charge (in Coulombs) \item \(I\) = electric current (in Amperes) \item \(t\) = time (in seconds) \end{itemize} This formula helps determine how much charge flows through a conductor when a steady current passes for a certain time. Step 1: {\color{red}Convert the given time into seconds.} \[ 10 \text{ minutes} = 10 \times 60 = 600 \text{ seconds} \] Step 2: {\color{red}Apply the formula \(Q = It\).} \[ Q = 2 \times 600 \] \[ Q = 1200 \,\text{C} \] Thus, the total charge flowing through the resistor is: \[ Q = 1200 \,\text{C} \] \bigskip

Answer 2

Concept:

• A current of 1 ampere already means 1 coulomb of charge flows every second, so it can be converted directly into a rate per minute instead of converting the given time into seconds.
• Charge is simply this rate multiplied by the number of minutes the current flows.

Step 1: Convert the current into charge flowing per minute.
$2\,A = 2$ coulombs per second $= 2 \times 60 = 120$ coulombs per minute.

Step 2: Multiply by the total number of minutes given.
$Q = 120 \times 10$

Step 3: Calculate the total charge.
$Q = 1200$

Final Answer: $Q = 1200\,C$