Physics - Capacitor Question with Solution | TestHub

PhysicsCapacitorCapacitanceMedium2 minQB

PhysicsMediuminteger

A parallel plate capacitor is filled by a di-electric whose relative permittivity varies with the applied voltage according to the law $= α V$ , where $α = 1$ per volt. The same (but containing no di-electric) capacitor charged to a voltage $V = 156$ volt is connected in parallel to the first "non-linear" uncharged capacitor. Determine the final voltage $V_{f}$ across the capacitors.

Answer:

Solution:

$Q = CV_{0} K = V$ $\frac{Q - q}{C} = \frac{q}{CV} = V [V$ is the final voltage] $\Rightarrow (Q - q) V = q \Rightarrow (CV_{0} - CV^{2}) V = CV^{2}$

$\Rightarrow VV_{0} - V^{3} = V^{2}$

$\Rightarrow V^{2} + V - V_{0} = 0$

$\Rightarrow V = \frac{- 1 \pm 1 + 4 V _{0}}{2} = \frac{- 1 + 25}{2} = 12 V$

Stream:JEESubject:PhysicsTopic:CapacitorSubtopic:Capacitance

⏱ 2mℹ️ Source: QB

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