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:
[tex]\[ 12 \text{ min} \times 60 \frac{\text{s}}{\text{min}} = 720 \text{ s} \][/tex]
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:
[tex]\[ Q = I \times t \][/tex]
where [tex]\( I \)[/tex] is the current (in amperes, A) and [tex]\( t \)[/tex] is the time (in seconds, s).
Given current [tex]\( I = 0.20 \)[/tex] A and time [tex]\( t = 720 \)[/tex] s, we have:
[tex]\[ Q = 0.20 \times 720 \][/tex]
[tex]\[ Q = 144 \text{ C} \][/tex]
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 [tex]\( e \)[/tex] of one electron is approximately:
[tex]\[ e = 1.602 \times 10^{-19} \text{ C} \][/tex]
Step 2: Calculate the number of electrons [tex]\( N \)[/tex].
The number of electrons [tex]\( N \)[/tex] that pass a point in the circuit can be calculated using the total charge [tex]\( Q \)[/tex] and the charge of a single electron [tex]\( e \)[/tex]:
[tex]\[ N = \frac{Q}{e} \][/tex]
Substituting the values we know:
[tex]\[ N = \frac{144}{1.602 \times 10^{-19}} \][/tex]
[tex]\[ N \approx 8.987 \times 10^{20} \][/tex]
So, approximately [tex]\( 8.987 \times 10^{20} \)[/tex] electrons pass the point in the circuit during this time.
