Circuit Calculations

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[edit] Parallel Circuit

If two or more circuit components are connected like the rungs of a ladder it is said they are connected in parallel. A parallel circuit is a different path for current through each of its components. A parallel circuit provides the same voltage across all its components, i.e. every component in a parallel circuit "sees" the same amount of voltage which is the total voltage.

For legs in parallel, calculating total resistance can be found using: 1/RT=1/R1+1/R2... and so on.

Voltage (V) and Current (I) are calculated similarly to circuits in series. In a parallel circuit current is added, so that IT= I1+I2... and so on.

For instance, let us assume a circuit with two parallel resistors of 50 ohms each. A battery provides 12 volts. The current of each leg of this circuit can be calculated as I=V/R, which is 12 volts/50 ohms and is 0.24 amps. Since the voltage is the same for both legs and in this example the resistors are equivalent as well, the current is also the same.

The power can be calculated as P=IV, where P=0.24 amps*12 volts, or 2.88 watts. For the above reasons the power is the same for both legs of this parallel circuit. When determining characteristics of circuits it is easier to think of each leg separately rather than as the interconnected system that it is.


[edit] Series Circuit

Voltage drops across a circuit in series so that total voltage (V) can be found by: VT=V1+V2+... and so on.

Current (I) across a series circuit stays the same. Total resistance can be determined as the sum of the resistances, so that RT=R1+R2... and so on.

As an example, for a system that has a 12 volt battery and two 50 ohm resistors in series, total resistance can be found as the sum of the resistances, or as 100 ohms. Total current can be found by IT=VT/RT, or IT=12V/100 ohms, or 0.12 amps.

Voltage across the resistors can be calculated using V=IR, or V=0.12 amps*50 ohms= 6 volts. The voltage is the same for both resistors since they are the same, and since they see the same amount of shared voltage from the battery. Power can be calculated as P=IV, or P=0.12 amps * 6V= 0.72 watts per resistor.

[edit] Notes

An important realization here is that the two 50 ohm resistors in parallel have more watts than the two 50 ohm resistors in series. This is because in a series circuit each resistor shares the total amount of electricity coming from the battery. This is as opposed to a parallel circuit, where each leg sees the full output of the battery.




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