A) A current of 4 A flows in a copper wire 10mm in diameter. The density of vale

Question

A) A current of 4 A flows in a copper wire 10mm in diameter. The density of valence electrons in copper is roughly 9 × 1028 m3 .

Find the drift speed of these electrons. The fundamental charge is 1.602 × 1019 C .

Answer in units of m/s.

B) A platinum resistance thermometer has a re- sistance of 200 when placed in an ice 0C bath and 143.6 when immersed in a crucible containing a melting substance.

What is the melting point of the substance? The temperature coefficient of the platinum is 0.00392(C)1. The resistor was calibrated at a temperature of 20C.

Answer in units of C.

Explanation / Answer

A) drift velocity Vd
Vd = I / nqA = 4/9 × 1028 *3.14* (5e-3)^2*1.602 × 1019 =3.53e-6 m/s
n is the number of charge carriers per m³
A is the cross sectional area on m²
q is the charge of the charge carriers (electrons)
q = –1.602e–19 Coulomb (charge on an electron)

B) Let : T0 = 20C,
R1 = 200 ,
T1 = 0C,
R = 143.6 and = 0.00392(C)1 .
The resistance at 20C is
R0 =(R1)/[1 + (T1 T0)]

=(200) / {1 + (0.00392(C)) * (0C 20C)}
= 217.014 ohms,

and

R = R0 [1 + (T T0)]
= R0 + R0 (T T0)
T T0 =(R R0) / R0
T = T0 + [(R R0) / (R0)]
T = 20C+[143.6 217.014 / (0.00392(C)) (217.014)]
= -66.30C

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