a potential difference of 3.40 nv is set up across a 2.00 cm length of copper wire which has a radius of 2.00 mm. how much charge drifts through a cross section in 3.80 ms?



Answer :

The amount of charge that drifts through the cross section in 3.80ms is 1.064* 10-13 C.

voltage (V) = 3.40nV  =  3.4*10-9 V                    

length (l) = 2.00cm = 0.2m

radius (r) = 2 mm = 0.002m

time (t) = 3.08 ms = 3.8*10-3 sec

resistivity of copper wire (ρ) = 1.62 * 108 Ωm

Area of cross section (A) = 2πr2

                A = 2 * 3.14 * 4 * 10,00,000

resistance (R) = ρ*l/A

                         =  (1.62 * 108 * 0.2)/( 2 * 3.14 * 4 * 10,00,000)

                     R  = 1.2 Ω

Ohm’s law gives the relationship between electric current and potential difference. The current that flows through conductors is directly proportional to the voltage applied to it.

Or mathematically it can be written as

I ∝ v

or

V = I R

I = V/R

I = (3.4 × 10⁻⁹) / 1.2

I = 2.8 nA

I = Q/t

Q = I×t

   = (2.8 ×10⁻⁹) × (3.8 × 10⁻³)

   = 1.064× 10⁻¹³ C

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