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A printed circuit board contains a resistor formed of a semicircular bend of resistive material (resistivity $\rho$) of thickness $t$, inner radius $a$ and outer radius $b$ as shown in the figure above. Copper traces maintain a constant voltage $V$ across the semicircular resistor. Find (in terms of the givens):

a) the resistance $R$ of the resistor - be sure to indicate the basic formulae you are starting from for partial credit in case you can't quite get the integral right (it is like the integral in a homework problem);

b) the energy dissipated as heat in the resistor in $s$ seconds. Again, if you cannot find $R$ in terms of the givens (or have little confidence in your answer), you may use $R$ and other given quantities to answer b) for at least partial credit.

Check the Units of Your Answers!


Robert G. Brown 2003-02-09