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TOPIC 15: Electric Circuits
To find the total resistance of several resistors connected in series, simply add up their resistances. This is pretty straight forward, as follows:
RT = R1 + R2 + R3
For resistances in parallel, some short-cut formulae exist which can save both time and effort.
We know that for resistances in parallel, let's say R1, R2 and R3, then:
1/RT = 1/R1 + 1/R2 + 1/R3
If the 3 resistors have the same value, eg. R, then:
1/RT = 1/R + 1/R + 1/R = 3/R
Hence, RT = R/3
In general, if there are N number of resistors R in parallel, their combined resistance is R/N
If two resistors R1 and R2 are in parallel, then:
1/RT = 1/R1 + 1/R2
1/RT = (R1 + R2)/(R1R2)
RT = (R1R2)/(R1 + R2)
ie. their combined resistance is equal to their product divided by their sum.
eg. resistors 3W and 6W are in parallel, their combined resistance is:
(3 x 6)/(3 + 6) = 18/9 = 2 W
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