Let's solve each part of the question step by step.
### Part a) Total Electric Charge
Step 1: Convert time from minutes to seconds.
Given that 1 minute is equal to 60 seconds, we first convert the 12 minutes to seconds:
\(\[ 12 \text{ min} \times 60 \frac{\text{s}}{\text{min}} = 720 \text{ s} \]\)
Step 2: Calculate the total electric charge (Q).
The total electric charge Q that passes a point in a circuit is given by the formula:
\(\[ Q = I \times t \]\)
where \(\( I \)\) is the current (in amperes, A) and \(\( t \)\) is the time (in seconds, s).
Given current \(\( I = 0.20 \)\) A and time \(\( t = 720 \)\) s, we have:
\(\[ Q = 0.20 \times 720 \]\)
\(\[ Q = 144 \text{ C} \]\)
So, the total electric charge which passes a point in the circuit in 12 minutes is 144 coulombs.
### Part b) Number of Electrons
Step 1: Use the charge of a single electron.
The charge \(\( e \)\) of one electron is approximately:
\(\[ e = 1.602 \times 10^{-19} \text{ C} \]\)
Step 2: Calculate the number of electrons \(\( N \)\).
The number of electrons \(\( N \)\) that pass a point in the circuit can be calculated using the total charge \(\( Q \)\) and the charge of a single electron \(\( e \)\):
\(\[ N = \frac{Q}{e} \]\)
Substituting the values we know:
\(\[ N = \frac{144}{1.602 \times 10^{-19}} \]\)
\(\[ N \approx 8.987 \times 10^{20} \]\)
So, approximately \(\( 8.987 \times 10^{20} \)\) electrons pass the point in the circuit during this time.
