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Question: How many coulombs are provided by a current of \[0.010\] \(mA\) in the calculator battery that can o...

How many coulombs are provided by a current of 0.0100.010 mAmA in the calculator battery that can operate for 10001000 hourshours?
A) 1.01.0
B) 1010
C) 0.0100.010
D) 3636

Explanation

Solution

Here we will use the basic definition of electric current and electric charge. Electric current may be defined as the electric charge flowing per unit time. To calculate the electric charge in coulombs, first convert the given quantities into standard units and then put the values in the formula.

Formula Used:
The formula used for calculating the electric charge is:
Q=I×tQ = I \times t
Where Q is electric charge, I is electric current and t is time of flow of current.

Complete step by step solution:
Step 1:
Convert the given current into SI units.
The SI unit of electric current is Ampere.
Here, we are given the amount of current as 0.0100.010 mA.
We know that 1mA=10−3A1mA = {10^{ - 3}}A
⇒0.010mA=0.010×10−3A ⇒I=10−5A  \Rightarrow 0.010mA = 0.010 \times {10^{ - 3}}A \\\ \Rightarrow I = {10^{ - 5}}A \\\
Step 2: Convert the given time into SI units.
The SI unit of time is second.
Here, we are given the time as 10001000 hours.
We know that 1hr=60×60s=3600s⁡1hr = 60 \times 60s = 3600\operatorname{s}
⇒1000hr=1000×3600s ⇒t=36×105  \Rightarrow 1000hr = 1000 \times 3600s \\\ \Rightarrow t = 36 \times {10^5} \\\
Step 3: Rearrange the formula of electric current.
1 ampere is equal to 1 coulomb per second.
So, the formula of electric current is I=QtI = \dfrac{Q}{t}
⇒Q=I×t\Rightarrow Q = I \times t

Step 4: Substitute the values of electric current and time in the calculated equation to get the value of electric charge:
Q=I×t ⇒Q=10−5×36×105 ⇒Q=36C  Q = I \times t \\\ \Rightarrow Q = {10^{ - 5}} \times 36 \times {10^5} \\\ \Rightarrow Q = 36C \\\
So, the value of electric charge provided by a current of 0.0100.010 mAmA in the calculator battery that can operate for 10001000 hourshours is 3636 CoulombCoulomb.

Hence, the correct answer is option (D), 3636.

Note: By simply multiplying the electric current with the given time, we get the amount of electric charge.
1. It should be noted that all the given quantities should be in the same system of units, either in the SI unit system or in the CGS unit system.
2. In the given question, we have to calculate the value of charge in Coulombs, which is the SI unit of electric charge.
3. So, we have converted time and current into their SI units, seconds and amperes respectively.