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quiz3_solution

# quiz3_solution - Answer I 1 = 0 353,I 2 = 0 118,I 3 = 0 471...

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solution to quiz3 1. In the Bohr model of the hydrogen atom, an electron in the lowest energy state moves at a speed of v = 2 . 19 × 10 6 m/s in a circular path of radius a B = 5 . 29 × 10 - 11 m . What is the effective current associated with this orbiting electron? Answer: 1 mA hint: The period of the circular motion is T = 2 πa B v so the current on average is I = Δ q Δ t = e T = 1 mA 2. Suppose that you wish to fabricate a uniform wire out of a m = 1 g of copper. If the wire is to have a resistance of R = 0 . 5Ω, and if all of the copper is to be used, what will be the length of this wire? (resistivity of copper is ρ r = 17 n Ω · m , density of copper is ρ = 9 g/cm 3 ) Answer: 1 . 8 m hint: For a copper wire of length l and cross-sectional area S , its resistance is R = ρ r l S on the other hand, l and S are related by the volume of the wire, lS = volume = m ρ so l = s mR ρρ r = 1 . 8 m 3. The output power of the Sun is 4 × 10 26 W . Calculate at eight cents per kilowatt-hour the cost of running the Sun for one second. Answer: 8 . 8 × 10 18 hint: cost = power of sun 1 × 10 3 W × (60 × 60) sec × 0 . 08 = 8 . 8 4. Find the current (in Ampere) in each resistor in Figure 1.

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Unformatted text preview: Answer: I 1 = 0 . 353 ,I 2 = 0 . 118 ,I 3 = 0 . 471 hint: The three segments share the same voltage drop, V 1-I 1 R 1 = V 2-I 2 R 2 = I 3 R 3 but by Kirchoﬀ’s theorem, I 1 + I 2 = I 3 we have 3 unknowns ( I 123 ) and 3 equations, so the problem can be uniquely solved. 1 5. Find the equivalent resistance between points a and b in Figure 2. Answer: 7 . 5Ω hint: R 2 and R 3 are in series, and their combination R 23 is in parallel with R 4 , and the whole triangle is in series with R 1 and R 5 . R ab = R 1 + R 234 + R 5 where R 234 = ( R 2 + R 3 ) R 4 R 2 + R 3 + R 4 6. An uncharged capacitor and a resistor are connected in series to a source of emf. If E = 9 V , C = 20 μF , and R = 100Ω, ﬁnd the time constant of the circuit Answer: 2 ms hint: The time constant doesn’t concern the emf. τ = RC = 2 ms 2 Fig 1 Fig 2 3...
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