A 12 V battery is connected to a network of resistors: a 6.0 Ω resistor in series with a parallel combination of a 12 Ω resistor and a 4.0 Ω resistor. What is the total current supplied by the battery?
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Correct answer
B. 1.33 A
Principle or equation
For resistors in series, the equivalent resistance is the sum. For resistors in parallel, the reciprocal of the equivalent resistance is the sum of the reciprocals. Ohm's law gives I = V/R_total.
Why this answer is correct
The parallel combination of 12 Ω and 4.0 Ω has equivalent resistance 1/R_par = 1/12 + 1/4 = 1/12 + 3/12 = 4/12 = 1/3, so R_par = 3.0 Ω. The total resistance is R_total = 6.0 Ω + 3.0 Ω = 9.0 Ω. The current is I = 12 V / 9.0 Ω = 1.33 A.
Example
If a 10 V battery is connected to a 2 Ω resistor in series with a parallel combination of 6 Ω and 3 Ω (which is 2 Ω), the total resistance is 4 Ω and the current is 2.5 A.
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