We have a copper wire 2m long and cross sectional area of 3x10^-8 m^2. a) What i

Question

We have a copper wire 2m long and cross sectional area of 3x10^-8 m^2.

a) What is the resistance of the wire?

My teachers answer was 1.12 ohms

b) If the wire is attached to a 20v battery, what is the current through the wire?

My teachers answer was 17.9 A

c) What is the power supplied to the wire?

My teachers answer was 358 J

d) How many electrons per second pass through a cross sectional area of the wire?

My teachers answer was 1.12x10^20

Please help me understand how he arrived at these answers. I will up-vote your answers and thank you!

Explanation / Answer

Length of wire L = 2 m , Cross sectional area A = 3*10-8 m2

a) For copper wire resistivity rho is 1.68*10-8 ohm m

Resistance of wire with length L, area A, and resistivity rho is Given by R = rho*L/A = 1.68*10-8 * 2 / 3*10-8 = 1.12 ohm

b) Voltage V = 20 V current is given by i = V/R = 20/1.12 = 17.86 A = 17.9 A

c) Power P = voltage * current (or current2 * resistance) = 20*17.9 = 358 W ( it will be Watt not Joule, Joule is work done Power is work done per unit time i.e. Watt)

d) Current i = 17.9 A, i = dq/dt , where q is charge. In one second total charge passed through wire = 17.9 C

Charge on one electron e = 1.6 * 10-19 C

Hence no. of electrons = total charge/ charge on one electron = 17.9 / (1.6 * 10-19 ) = 1.118 * 1020 = 1.12 * 1020

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