Volts, & Ohms
Bob has 3 resistors. They are 10 ohms, a 20 ohms, and a 30 ohms. He can connect them to a 12 volt battery in 3 different circuits where one resistor is in series with the other two in parallel to each other. If the current in each circuit is a amps, b amps, and c amps, find a + b + c to two decimal places.
The answer is 1.31.
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1 solution
Case A: 10 ohm in series with 20 ohm and 30 ohm in parallel. Eqv. resistance of 20 and 30 is 20X30/(20+30) = 12.
Total Resistance = 10 + 12 = 22 ohms
I = 12/22 = 6/11 = 30/55 Amps = a
Case B: 20 ohm in series with 10 ohm and 30 ohm in parallel. Eqv. resistance of 10 and 30 is 10X30/(10+30) = 7.5
Total Resistance = 20 + 7.5 = 27.5
I = 12 / 27.5 = 24 / 55 Amps = b
Case C: 30 ohm in series with 10 ohm and 20 ohm in parallel. Eqv. resistance of 10 and 20 is 10X20/(10 + 20) = 6 2/3
Total Resistance = 30 + 6 2/3 = 36 2/3
I = 12 / 36 2/3 = 18/55 Amps = c
a + b + c = 72 / 55 = 1.31 Amps