Resistors and how to calculate effective resistance?

Resistors are often connected together in a circuit, so it is necessary to know how to determine the resistance of a combination of two or more resistors. There are two basic ways in which resistors can be connected: in series and in parallel.

Determining the total resistance for two or more resistors in series is very simple. Total resistance equals the sum of the individual resistances. In this case, RT=R1+R2+R3 . This makes common sense; if you think again in terms of water flow, a series of obstructions in a pipe add up to slow the flow more than any one. The resistance of a series combination is always greater than any of the individual resistors

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Some of the total current will flow through R1 and some will flow through R2, causing an equal voltage drop across each resistor. More current, however, will flow through the path of least resistance. The formula for total resistance in a parallel circuit is more complex than for a series circuit:

                                                   RT={1{1R1}+{1R2}...+{1Rn}}