Final answer:
The current through each parallel branch consisting of a 10-ohm resistor and a 9-V battery is 0.9 A. The total current from the battery is equal to 0.9 A multiplied by the number of resistors. Hence, with 28 resistors in parallel, the current from the battery would be 25.2 A.
Step-by-step explanation:
The student asks us to construct circuits with a 9-V battery and 10-ohm resistors in parallel, and consider configurations with 1, 2, 3, and 4 resistors.
Then, infer a pattern for how the current through one branch relates to the number of resistors in the circuit and determine the current from the battery when there are 28 resistors in parallel.
When resistors are connected in parallel, the voltage across each resistor is the same and equal to the battery voltage, in this case, 9 V. According to Ohm's Law, V = I x R, the current through each resistor is V/R. For a 10-ohm resistor, this would be 9V/10Ω = 0.9 A. When resistors are added in parallel, each additional resistor provides another path for the current to take, which increases the total current supplied by the battery in proportion to the number of resistors.
So, for one resistor, the battery supplies 0.9 A. For two resistors, each would draw 0.9 A, and the total current would be 0.9 A + 0.9 A = 1.8 A. For n resistors, the current from the battery would be 0.9 A * n. For 28 resistors, the total current from the battery would be 0.9 A * 28 = 25.2 A.