Biyernes, Hulyo 11, 2014

BASIC LAW: Series and Parallel Resistors

SERIES CIRCUIT
- In a series circuit, the current through each of the components is the same, and the voltage across the circuit is the sum of the voltages across each component. In a parallel circuit, the voltage across each of the components is the same, and the total current is the sum of the currents through each component.

A series circuit with a voltage source (such as a battery) and 3 resistors



Current
        I = I_1 = I_2 = \dots = I_n
In a series circuit the current is the same for all elements.

Resistors
The total resistance of resistors in series is equal to the sum of their individual resistances:
 
This is a diagram of several resistors, connected end to end, with the same amount of current through each.



PARALLEL CIRCUIT
- If two or more components are connected in parallel they have the same potential difference (voltage) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities. The same voltage is applicable to all circuit components connected in parallel. The total current is the sum of the currents through the individual components, in accordance with Kirchhoff’s current law.



 

 Circuit containing resistors in parallel


Voltage
V = V_1 = V_2 = \ldots = V_n
In a parallel circuit the voltage is the same for all elements.

Resistors
I_\mathrm{total} = V\left(\frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n}\right)
The current in each individual resistor is found by Ohm's law. Factoring out the voltage gives

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