Question

A wire with a radius R = .89 mm and length 45 cm is made of two materials, Carbon and Nichrome (resistivity not given I assume it needs to be googled). The Carbon portion is 15 cm long. The temperature of the wire is 75 ^oC. The wire is connected to a 12 volt battery.

a) Find the total Resistance of the battery as well as the current (I) and the current density (J) and the electric field (E) in the wire.

b) Find the power dissipated in the wire (P) and the power delivered by the battery.

c) At what temperature is the total resistance of the wire 1 ohm less than at 20 Celsius?

Answers should be:

a) R = 2.24 Ω I = 5.36 amps, J = 2.15 Mamps/m², E = 26.67 V/m

b) P_resistor = 64.35 watts, P_battery = 64.35 watts

c) T = 1037.77 Celsius

Answer 1

(1) radius of wire r = 0.00089 m

total length of wire L = 0.45 m

length of carbon wire Lc = 0.15 m

length of nichrome wire Ln = 0.30 m

resistivity of copper wire = 35 x 10^{-6} ohm.m

resistivity of nichrome wire = 1.5 x 10^{-6} ohm.m

wire is connected to 12 Volt battery.

(A) Since wires are connected in series therefore net resistance of wire is the sum of resistance made by carbon and nichrome wire, thus;

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apply ohms law to find current in the wire;

V = IR;

I = 12/2.23 = 5.36 A

I = 5.36 A

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current density (J);

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Electric field (E);

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(B) power dissipated in the wire;

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power delivered by the battery is same as dissipated power;

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