Parallel Circuits - the Plague!R _{ 1 } = 50 Ω R _{ 2 } = 200 Ω A _{ 1 } reads .2 Amps in current ( I=.2 ) Find: Total Voltage Total Circuit Resistance Total Current And Finally, the Current through A _{ 2 } Now this isn't as tuff as it first looks. Let's break the problem down. We know according to Ohm's law, that if we know the resistance and current, we can find the voltage. E _{ R1 } = I _{ R1 } x R _{ 1 } . E = .2 x 50 = 10 E = 10 Volts. Now that we know that the voltage for the entire circuit is 10 volts, let's find the total Resistance. First, we find the reciprocals of the individual resistances: R _{ 1 } = 50 ohms. 1/50 = .02 R _{ 2 } = 200 ohms. 1/200 = .005 Now we add the two reciprocals together: .02 + .005 = .025 Finally we take the reciprocal of the sum: 1 / .025 = 40 Ω So if the Total Voltage of the circuit is 10 Volts, and the Total Resistance = 40 Ω then by using Ohms Law again we can find the total current. I _{ Total } = E _{ Total } / R _{ Total } I = 10/40 = ¼ Ampere. Almost finished now. So far we know: R _{ 1 } = 50 Ω R _{ 2 } = 200 Ω A _{ 1 } reads .2 Amps in current ( I=.2 ) V _{ Total } = 10 R _{ Total } = 40 and I _{ Total } = ¼ Now we have at least 2 methods by which we can find the current through A _{ 2 } . We know that the Total current is the sum of all the individual leg currents, so if we subtract the current of A _{ 1 } from the Total current we get this: I _{ Total } - I _{ 1 } = I _{ 2 } .25 - .2 = I _{ 2 } = .05 Amperes. The other method would be by using Ohms Law. We know the resistance of R _{ 2 } = 200 Ω. We also know that the voltage across R _{ 2 } = 10 Volts. Hence: 10 Volts / 200 Ω = .05 Amperes. Either way, our final result is A _{ 2 } = .05 Amps |
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