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A high impedance probe with 9MΩ resistance and 4 pF capacitance is connected to an oscilloscope with an input resistance of 1MΩ. If the effective capacitance is now decreased to 3.6 pF when the probe was connected, the capacitance of the oscilloscope alone in Pico-Farads is _____.
Correct answer is '36'. Can you explain this answer?
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A high impedance probe with 9M resistance and 4 pF capacitance is conn...
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Now, the probe-oscilloscope step can be represented as,
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A high impedance probe with 9M resistance and 4 pF capacitance is conn...
Given:
- High impedance probe resistance (Rp) = 9MΩ
- High impedance probe capacitance (Cp) = 4 pF
- Oscilloscope input resistance (Ro) = 1MΩ
- Effective capacitance with probe connected (Ceff) = 3.6 pF
To find:
- Capacitance of the oscilloscope alone (Co) in picofarads (pF)
Explanation:
When the high impedance probe is connected to an oscilloscope, it forms a capacitive voltage divider with the oscilloscope's input capacitance. The effective capacitance is given by the formula:
Ceff = Cp * (Ro / (Ro + Rp))
To find the capacitance of the oscilloscope alone, we rearrange the formula:
Ceff = Cp * (Ro / (Ro + Co))
Solving the equation:
Substituting the given values:
3.6 pF = 4 pF * (1MΩ / (1MΩ + Co))
Dividing both sides by 4 pF:
0.9 = 1MΩ / (1MΩ + Co)
Cross-multiplying:
0.9 * (1MΩ + Co) = 1MΩ
Expanding the equation:
0.9MΩ + 0.9Co = 1MΩ
Subtracting 0.9MΩ from both sides:
0.9Co = 1MΩ - 0.9MΩ
Simplifying:
0.9Co = 0.1MΩ
Dividing both sides by 0.9:
Co = (0.1MΩ) / 0.9
Co = 0.111111... MΩ
Converting to picofarads (pF):
Co = 0.111111... * 1000 pF
Co ≈ 111.111... pF
Rounding to the nearest whole number:
Co ≈ 111 pF
The capacitance of the oscilloscope alone is approximately 111 pF.
- High impedance probe resistance (Rp) = 9MΩ
- High impedance probe capacitance (Cp) = 4 pF
- Oscilloscope input resistance (Ro) = 1MΩ
- Effective capacitance with probe connected (Ceff) = 3.6 pF
To find:
- Capacitance of the oscilloscope alone (Co) in picofarads (pF)
Explanation:
When the high impedance probe is connected to an oscilloscope, it forms a capacitive voltage divider with the oscilloscope's input capacitance. The effective capacitance is given by the formula:
Ceff = Cp * (Ro / (Ro + Rp))
To find the capacitance of the oscilloscope alone, we rearrange the formula:
Ceff = Cp * (Ro / (Ro + Co))
Solving the equation:
Substituting the given values:
3.6 pF = 4 pF * (1MΩ / (1MΩ + Co))
Dividing both sides by 4 pF:
0.9 = 1MΩ / (1MΩ + Co)
Cross-multiplying:
0.9 * (1MΩ + Co) = 1MΩ
Expanding the equation:
0.9MΩ + 0.9Co = 1MΩ
Subtracting 0.9MΩ from both sides:
0.9Co = 1MΩ - 0.9MΩ
Simplifying:
0.9Co = 0.1MΩ
Dividing both sides by 0.9:
Co = (0.1MΩ) / 0.9
Co = 0.111111... MΩ
Converting to picofarads (pF):
Co = 0.111111... * 1000 pF
Co ≈ 111.111... pF
Rounding to the nearest whole number:
Co ≈ 111 pF
The capacitance of the oscilloscope alone is approximately 111 pF.
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A high impedance probe with 9M resistance and 4 pF capacitance is connected to an oscilloscope with an input resistance of 1M. If the effective capacitance is now decreased to 3.6 pF when the probe was connected, the capacitance of the oscilloscope alone in Pico-Farads is _____.Correct answer is '36'. Can you explain this answer?
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A high impedance probe with 9M resistance and 4 pF capacitance is connected to an oscilloscope with an input resistance of 1M. If the effective capacitance is now decreased to 3.6 pF when the probe was connected, the capacitance of the oscilloscope alone in Pico-Farads is _____.Correct answer is '36'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A high impedance probe with 9M resistance and 4 pF capacitance is connected to an oscilloscope with an input resistance of 1M. If the effective capacitance is now decreased to 3.6 pF when the probe was connected, the capacitance of the oscilloscope alone in Pico-Farads is _____.Correct answer is '36'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A high impedance probe with 9M resistance and 4 pF capacitance is connected to an oscilloscope with an input resistance of 1M. If the effective capacitance is now decreased to 3.6 pF when the probe was connected, the capacitance of the oscilloscope alone in Pico-Farads is _____.Correct answer is '36'. Can you explain this answer?.
A high impedance probe with 9M resistance and 4 pF capacitance is connected to an oscilloscope with an input resistance of 1M. If the effective capacitance is now decreased to 3.6 pF when the probe was connected, the capacitance of the oscilloscope alone in Pico-Farads is _____.Correct answer is '36'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A high impedance probe with 9M resistance and 4 pF capacitance is connected to an oscilloscope with an input resistance of 1M. If the effective capacitance is now decreased to 3.6 pF when the probe was connected, the capacitance of the oscilloscope alone in Pico-Farads is _____.Correct answer is '36'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A high impedance probe with 9M resistance and 4 pF capacitance is connected to an oscilloscope with an input resistance of 1M. If the effective capacitance is now decreased to 3.6 pF when the probe was connected, the capacitance of the oscilloscope alone in Pico-Farads is _____.Correct answer is '36'. Can you explain this answer?.
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A high impedance probe with 9M resistance and 4 pF capacitance is connected to an oscilloscope with an input resistance of 1M. If the effective capacitance is now decreased to 3.6 pF when the probe was connected, the capacitance of the oscilloscope alone in Pico-Farads is _____.Correct answer is '36'. Can you explain this answer?, a detailed solution for A high impedance probe with 9M resistance and 4 pF capacitance is connected to an oscilloscope with an input resistance of 1M. If the effective capacitance is now decreased to 3.6 pF when the probe was connected, the capacitance of the oscilloscope alone in Pico-Farads is _____.Correct answer is '36'. Can you explain this answer? has been provided alongside types of A high impedance probe with 9M resistance and 4 pF capacitance is connected to an oscilloscope with an input resistance of 1M. If the effective capacitance is now decreased to 3.6 pF when the probe was connected, the capacitance of the oscilloscope alone in Pico-Farads is _____.Correct answer is '36'. Can you explain this answer? theory, EduRev gives you an
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