An oscilloscope has an input resistance of \( 1\, {M}\Omega \). A 10X passive attenuating probe is connected to it to increase the input voltage range as well as the effective input resistance. The effective input resistance, in \( {M}\Omega \), seen into the probe tip is:
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- \( 0.9 \)
- \( 9.1 \)
- \( 10 \)
- \( 11 \)
The Correct Option is C
Solution and Explanation
Step 1: Understanding the probe configuration.
A 10X passive probe attenuates the voltage by a factor of 10. This is achieved using a resistor in the probe (say \( R_p \)) and the oscilloscope's internal input resistance \( R_{{scope}} \) arranged in a voltage divider.
Step 2: Determine the resistor values.
To get 10X attenuation: \[ \frac{R_{{scope}}}{R_p + R_{{scope}}} = \frac{1}{10} \Rightarrow \frac{1\,{M}\Omega}{R_p + 1\,{M}\Omega} = \frac{1}{10} \] Solving: \[ 10 = \frac{R_p + 1}{1} \Rightarrow R_p = 9\,{M}\Omega \] Step 3: Effective input resistance seen into the probe tip.
The total resistance from the probe tip into the oscilloscope is the series combination of: \[ R_{{effective}} = R_p + R_{{scope}} = 9 + 1 = 10\,{M}\Omega \]
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