# 關於物理的簡單問題(2)

1. A cell of internal resistance r is connected to a load of resistance R.

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Energy is dissipated in the load, but some thermal energy is also wasted in the cell. The efficiency of such an arrangement is found from the expression

Energy dissipated in the complete circuit.

Which of the following gives the efficiency in this case?

The answer is R / (R + r).

2. A ray of light travels from air to glass as shown.

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The speed of light in air is 3.00 x 10^8 ms^-1.

What is the speed of light in the glass?

The answer is 2.12 x 10^8 ms^-1.

3. Which of the following operation may affect the frequency of the a.c. output in an a.c. generator?

(1) To increase the magnetic field.

(2) To increase the turns of coil.

(3) To increase the rate of revolution.

4. Water waves of wavelength 4 m are produced by two vibrators, S1 and S2, as shown. Each vibrator, when operated by itself, produces waves which have an amplitude A at X, which is 3 m from S1 and 5 m from S2.

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When the vibrators are operated in phase, what is the amplitude of oscillation at X?

※試列明計算步驟及詳盡解釋其答案之原因※

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1. Let I be the current flowing through the circuit.

Energy dissipated on the circuit = I^(R+r)

Energy dissipated on load = I^2.R

Hence, efficiency = I^.R/I^2(R+r) = R/(R+r)

2. Refractive index n = sin(45)/sin(30) = 1.414

Since n = speed of light in air/speed of light in glass

1.414 = 3 x 10^8/speed of light in glass

i.e. speed of light in glass = 3x10^8/1.414 m/s = 2.12 x 1-^8 m/s

3. Magnetic field and no. of turns of the coil only affect the output voltage. The rotational speed of the coil determines the output frequency.

4. Path difference = (5 - 3 ) m = 2 m

Hence, the path difference is half of the wavelength of 4 m. Destructive interference occurs at X.

The amplitude of vibration is therefore zero.

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