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JEE Advanced 2020Paper 2
Exam
JEE Advanced
Year
2020
Paper
Paper 2
Subject
Physics
Chapter
Mathematics in Physics

JEE Advanced 2020 · Paper 2 · Physics · Mathematics in Physics

Two capacitors with capacitance values C _ 1 = (2000 ± 10)pF and C...

Two capacitors with capacitance values C1=(2000±10)pF{C}_{1} = \left(2000 \pm 10\right)pF and C2=(3000±15)pF{C}_{2} = \left(3000 \pm 15\right)pF are connected in series. The voltage applied across this combination is V=(5.00±0.02)VV = \left(5 . 00 \pm 0 . 02\right)V. The percentage error in the calculation of the energy stored in this combination of capacitors is __________.

Correct answer

0

Step-by-step solution

For the purpose of calculation of error, fundamental formula is considered

1C=1C1+1C2⇒C=1200pF\dfrac{1}{C} = \dfrac{1}{{C}_{1}} + \dfrac{1}{{C}_{2}} ⇒ C = 1200pF

−dCC12=−dC1C12−dC2C22- dC{C}_{1}^{2} = - d{C}_{1}{C}_{1}^{2} - d{C}_{2}{C}_{2}^{2}

dC=6pFdC = 6pF

Equivalent capacitance =(1200±6)pF= \left(1200 \pm 6\right)pF

E=1/2CV2E = 1 / 2{CV}^{2}

(dE/E=dC/C+2dV/V)×100( dE / E = dC / C + 2dV / V ) \times 100

=1.3= 1 . 3 %

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