KVPY 2020-21 SA Exam Previous Papers

Question : 28 of 80

Marks: +1, -0

A student was trying to construct the circuit shown in the figure below marked (a), but ended up constructing the circuit marked (b). Realizing her mistake, she corrected the circuit, but to her surprise, the output voltage (across R) did not change.

The value of resistance R is

100 Ω
150 Ω
200 Ω
300 Ω

Validate

Solution:

. (a)

R_{\text "eff"}={300 R}/{300+R}+300

R_{\text "eff"}=({300 R+300 R+90000}/{300+R})

I={V}/{R_{\text "eff "}}

={(300+R) \×10}/{(600 R+90000)}

(V_{R})_{1}={(300+R) \×10}/{(600 R+90000)} \×{300}/{(300+R)} \×R

(V_{R})_{1}={10 R}/{(2 R+300)}

(b)

R_{{\eff}}={(200+R) \× 300}/{(500+R)}+100

={60000+300 R+100 R+50000}/{500+R}

R_{{\eff}}={110000+400 R}/{500+R}

I=-{V}/{R_{\text"eff "}}

I={10 \×(500+R)}/{(110000+400 R)}

(V_{R})_{2}={300 \×(5000+10 R) \×R}/{(110000+400 R) \×(500+R)}

(V_{R})_{2}={3000 R}/{(110000+400 R)}

(V_{R})_{2}={30 R}/{(1100+4 R)}

(V_{R})_{1}=(V_{R})_{2}

{10 R}/{(2 R+300)}={30 R}/{(400+4 R)}

6 R+900=1100+4 R

R=100 \Ω

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