Sabtu, 12 Februari 2011

Series and parallel resistors

In a series configuration, the current through all of the resistors is the same, but the voltage across each resistor will be in proportion to its resistance. The potential difference (voltage) seen across the network is the sum of those voltages, thus the total resistance can be found as the sum of those resistances:
A diagram of several resistors, connected end to end, with the same amount of current going through each
R_\mathrm{eq} = R_1  + R_2 + \cdots + R_n
As a special case, the resistance of N resistors connected in series, each of the same resistance R, is given by NR.
Resistors in a parallel configuration are each subject to the same potential difference (voltage), however the currents through them add. The conductances of the resistors then add to determine the conductance of the network. Thus the equivalent resistance (Req) of the network can be computed:
A diagram of several resistors, side by side, both leads of each connected to the same wires
\frac{1}{R_\mathrm{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots +  \frac{1}{R_n}
The parallel equivalent resistance can be represented in equations by two vertical lines "||" (as in geometry) as a simplified notation. For the case of two resistors in parallel, this can be calculated using:
R_\mathrm{eq} = R_1 \| R_2 = {R_1 R_2 \over R_1 + R_2}
As a special case, the resistance of N resistors connected in parallel, each of the same resistance R, is given by R/N.
A resistor network that is a combination of parallel and series connections can be broken up into smaller parts that are either one or the other. For instance,
A diagram of three resistors, two in parallel, which are in series with the other
R_\mathrm{eq} = \left( R_1 \| R_2 \right) + R_3 = {R_1 R_2 \over R_1 + R_2} + R_3

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