GATE 2025 IN Q.26: solution and answer

GATE 2025 · INQ.26 · 1 mark · MCQ

An oscilloscope has an input resistance of $1 M Ω$ . 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 $M Ω$ , seen into the probe tip is

(A)
0.9
(B)
9.1
(C)
10
(D)
11

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Answer and solution

ANSWER

The effective input resistance seen into the probe tip is $10 M Ω$ , which is option (C).

Official answer: CSource: Official answer key, GATE 2025 IN (IIT Roorkee)

A passive 10X probe puts a resistor $R_{p}$ in series with the oscilloscope's input resistance $R_{in} = 1 M Ω$ . The two resistors form a voltage divider, and the oscilloscope sees only the voltage across $R_{in}$ .
The attenuation equals the divider ratio: $\frac{V _{t i p}}{V _{sco p e}} = \frac{R _{p} + R _{in}}{R _{in}} = 10$
Solve for the probe resistor, working in $M Ω$ : $R_{p} + 1 = 10 \Rightarrow R_{p} = 9 M Ω$ .
Looking into the probe tip, the two resistors are in series, not in parallel: $R_{t i p} = R_{p} + R_{in} = 9 + 1 = 10 M Ω$
Check: the oscilloscope sees $V_{t i p} /10$ , so the usable input voltage range goes up by a factor of 10. The resistance loading the circuit under test also goes up by a factor of 10, so the probe draws less current. These are the two effects the question describes. The probe's compensation capacitor is trimmed so that $R_{p} C_{p} = R_{in} C_{in}$ . It sets the frequency response and does not change the dc resistance.
Effective input resistance $= 10 M Ω$ , which is option (C).

KEY IDEA

A 10X passive probe is a series resistor $R_{p} = 9 R_{in}$ that forms a 10:1 divider with the oscilloscope's input resistance. At the tip, $R_{p}$ and $R_{in}$ are in series, so the tip resistance is $R_{p} + R_{in} = 10 R_{in}$ . The attenuation factor and the factor by which the input resistance rises are the same number.

WATCH OUT FOR

One mistake is to combine $R_{p} = 9 M Ω$ and $R_{in} = 1 M Ω$ in parallel, which gives $0.9 M Ω$ (option A). The other is to report only the probe resistor, $9 M Ω$ , or to guess $R_{in} (1 + 1/10)$ . The current from the tip passes through $R_{p}$ and then through $R_{in}$ , so the two resistors are in series and the total is $10 M Ω$ .

From the GATE 2025 IN paper. Every question of this paper · Download the full paper · All 5 Time, frequency & scopes questions, with notes

GATE 2025 IN Q.26: solution and answer

Answer and solution

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