The circuit shown above is used to measure the size of the capacitance C. The y-coordinate of the spot on the oscilloscope screen is proportional to the potential difference across R, and the x-coordinate of the spot is swept at a constant speed s. The switch is closed and then opened. One can then calculate C from the shape and the size of the curve on the screen plus a knowledge of which of the following?
A. V0 and R
B. s and R
C. s and V0
D. R and R'
E. The sensitivity of the oscilloscope
(GR9277 #86)
Solution:
The voltage of a capacitor follows an exponential decay:
V(t) = V0e−t/RC
C depends on V(t), V0, t, and R.
V0 is given and known from the beginning of measurement.
The y-coordinate of the spot on the oscilloscope screen is proportional to the potential difference across R. Thus, V(t) is the shape and the size of the curve on the screen.
The x-coordinate of the spot is swept at a constant speed s. From this we can calculate time t.
Therefore, we can calculate C from the shape and the size of the curve plus a knowledge of s and R.
Answer: B
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