1A wire has a diameter of 60 mm and a length of 33 m and is

1)A wire has a diameter of 6.0 mm and a length of 33 m, and is found to have a resistance of 1.3 . What is the resistivity of the wire? · m

2)A 9.6-V battery for a cordless drill can supply 5.0 A of current.

(a) If the drill is continuously operated for 4 min, what is the total charge passing through the battery?
C

(b) What total amount of work does the battery do on the charge during these 4 min?
J

Solution

1) We know that resistivity = (R*A)/L, where R is the resistance, A is the area of cross section and L is the length of the conductor.

R = 1.3 Ohm (given), L = 33 m (given), diameter (d) = 6 mm = 0.006 m

Area of cross section ( since a wire has a circular cross section) = d²/4;

So A = 3.14*(0.006)²/4 = 0.00002826 m²

So, resistivity = (R*A)/L = 1.3*0.00002826/33 = 0.0000011133 Ohm-m

2)

a) Current = Charge/time, or charge = current*time

Current provided by the battery = 5 A

Time for which the drill operates = 4 min = 4*60 = 240 s

So, charge flown through the drill = 5*240 C = 1200 C

b)

Amount of work done by battery = V*I*t , where V= voltage of the battery, I = current supplied by the battery, t= time duration for which this current is supplied

V= 9.6 V, I = 5A, t = 4 min = 4*60 s = 240 s (given)

So, Work done = 9.6*5*240 = 11520 J