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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
Capacitors

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Capacitors

The capacitance between adjacent plates in a three-plate...

The capacitance between adjacent plates in a three-plate arrangement is 50extnF50 ext{ nF}. A charge of 1.0extμC1.0 ext{ }\mu\text{C} is placed on the middle plate. Calculate the potential difference developed between the upper and the middle plates.
The capacitance between adjacent plates in a three-plate arrangement is 50 ext nF . A charge of 1.0 ext is placed on

Options

  1. A0extV0 ext{ V}
  2. B20extV20 ext{ V}
  3. C10extV10 ext{ V}
  4. D5.0extV5.0 ext{ V}

Correct answer

C. 10extV10 ext{ V}

Step-by-step solution

Let the charge given to the middle plate be Q=1.0μCQ = 1.0 \mu\text{C}.

By symmetry, the charge QQ distributes equally on the two faces of the middle plate. Therefore, the charge on the upper face of the middle plate is q=Q2=0.5μCq = \dfrac{Q}{2} = 0.5 \mu\text{C}.

The upper plate and the middle plate act as a parallel plate capacitor with capacitance C=50 nFC = 50 \text{ nF}.

The potential difference VV between the upper and middle plates depends on the charge on their facing surfaces.

Using the relation V=qCV = \dfrac{q}{C}:

V=0.5×10−650×10−9=500×10−950×10−9=10 VV = \dfrac{0.5 \times 10^{-6}}{50 \times 10^{-9}} = \dfrac{500 \times 10^{-9}}{50 \times 10^{-9}} = 10 \text{ V}
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