Circuits physics question?

Question

A 160 uF capacitor charged to 450 V is discharged through a 31.2 k ohms resistor. What is the time constant? What is the temperature increase of the resistor, given its mass is 2.50 g and its specific heat is 0.400 cal/g degree celcius, most of the heat is retained in the short time of the discharge. What is the new resistance, assuming it is pure carbon?

Answer 1

T = RC = 31.2k x 160uF = 4992 ms = 4.99 sec

Energy in a cap is

E = ½CV²

E = ½(160u)450² = 16.2 J

E = 0.400 cal/gC x ΔT

16.2 J = 0.400 cal/gC x 2.5g x ΔT

ΔT = 16.2/0.4*2.5

ΔT = 16.2 C

I can't find a reliable number for the temp coef of carbon, but use that with the 16C temp change to calculate the resistance change.

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