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I need the formula for calculating resistor wattage when the resistors are in series. For example, say I have 3 1/4 watt 10 ohm resistors in series. What is the potential power dissipation for the entire circuit?

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Since resistors are in series, the current will be the same throughout the chain. Assuming that the voltage V across the string of resistors is constant, you can calculate the current \$I={V \over R_1+R_2 +R_3+ ...}\$. Power dissipated on each of the resistors: \$P_i=I^2R_i\$. If \$P_i\$ is less than the power rating of the resistor, it should dissipate the power without burning.

A string of N identical resistors in series each rated for P watts can dissipate \$NP\$ watts.

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Nice and simple. Great explanation! – Matt Mar 19 '12 at 2:34
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Twinkle, twinkle little star, power = i^2 r :-) – JonnyBoats Mar 19 '12 at 3:04
Nice... I don't think I'll be forgetting that one any time soon. =) – Matt Mar 19 '12 at 3:37
A uniform series or parallel string of identical resistors can dissipate NP watts. The word identical is important, though. Each resistor's contribution to dissipation will be proportional to its resistance, so a 1K 1W in series with a 2K 1W would only dissipate 1½W total (though one could use 1K ½W in series with a 2K 1W and get total power dissipation equal to the sum of the individual ones). – supercat Mar 19 '12 at 14:44

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