An oscilloscope input impedance consists of $1 M Ω$ resistance connected in parallel with a $100 p F$ capacitor. A compensted $20 : 1$ attenuator is obtained by connecting a parallel combination of ___.

19 M Ω a n d \frac{100}{19} p F

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200 M Ω a n d \frac{100}{20} p F

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19 M Ω a n d 1900 p F

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19 M Ω a n d 2000 p F

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Solution

The correct option is A $19 M Ω a n d \frac{100}{19} p F$

$R_{1} = 1 M Ω$

$C_{2} = 100 p F$

$\frac{R_{2}}{R_{1} + R_{2}} = \frac{1}{20}$

$\frac{1}{R_{1} + 1} = \frac{1}{20}$

$R_{1} + 1 = 20$

$∴ R_{1} = 19 M Ω$

$\frac{C_{1}}{C_{1} + C_{2}} = \frac{1}{20}$

$\frac{C_{1}}{C_{1} + 100} = \frac{1}{20}$

$20 C_{1} = C_{1} + 100$

$19 C_{1} = 100$

$C_{1} = \frac{100}{19} p F$

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