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Current Electricity question

2023 · 29 Jan · Shift 2 · Q70
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Current Electricity question

2023 · 29 Jan · Shift 2 · Q70

JEE MainPhysicsCurrent ElectricityNumerical+4 / −1
When two resistance R1\mathrm{R_1}R1​ and R2\mathrm{R_2}R2​ connected in series and introduced into the left gap of a meter bridge and a resistance of 10 Ω\OmegaΩ is introduced into the right gap, a null point is found at 60 cm from left side. When R1\mathrm{R_1}R1​ and R2\mathrm{R_2}R2​ are connected in parallel and introduced into the left gap, a resistance of 3 Ω\OmegaΩ is introduced into the right gap to get null point at 40 cm from left end. The product of R1R2\mathrm{R_1}\mathrm{R_2}R1​R2​ is ‾\underline{\hspace{2cm}}​Ω2\Omega^2Ω2
Numerical answer
View written solutionFree

Correct answer: 30

  1. Use meter bridge balance condition

For a meter bridge at balance,

RleftRright=l100−l\frac{R_{\text{left}}}{R_{\text{right}}}=\frac{l}{100-l}Rright​Rleft​​=100−ll​

where lll is the balancing length from the left end.

  1. First case: R1R_1R1​ and R2R_2R2​ in series

Then left-gap resistance is

Rs=R1+R2R_s=R_1+R_2Rs​=R1​+R2​

Right-gap resistance is 10 Ω10\,\Omega10Ω.

Null point is at 60 60\,60cm from the left, so

R1+R210=6040=32\frac{R_1+R_2}{10}=\frac{60}{40}=\frac{3}{2}10R1​+R2​​=4060​=23​

Hence,

R1+R2=10⋅32=15 ΩR_1+R_2=10\cdot \frac{3}{2}=15\,\OmegaR1​+R2​=10⋅23​=15Ω
  1. Second case: R1R_1R1​ and R2R_2R2​ in parallel

Then left-gap resistance is

Rp=R1R2R1+R2R_p=\frac{R_1R_2}{R_1+R_2}Rp​=R1​+R2​R1​R2​​

Right-gap resistance is 3 Ω3\,\Omega3Ω.

Null point is at 40 40\,40cm from the left, so

Rp3=4060=23\frac{R_p}{3}=\frac{40}{60}=\frac{2}{3}3Rp​​=6040​=32​

Therefore,

Rp=3⋅23=2 ΩR_p=3\cdot \frac{2}{3}=2\,\OmegaRp​=3⋅32​=2Ω

So,

R1R2R1+R2=2\frac{R_1R_2}{R_1+R_2}=2R1​+R2​R1​R2​​=2

Using R1+R2=15R_1+R_2=15R1​+R2​=15,

R1R215=2\frac{R_1R_2}{15}=215R1​R2​​=2

Thus,

R1R2=30 Ω2R_1R_2=30\,\Omega^2R1​R2​=30Ω2
  1. Final answer
30\boxed{30}30​
  1. Comparison with stored answer

Stored correct answer = 303030.

So, the derived answer agrees with the stored answer.

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