Question 189: Electrostatics & Capacitance

Question

Three parallel plate capacitors $C_1, C_2$ and $C_3$ each of capacitance $5 \mu \mathrm{~F}$ are connected as shown in figure. The effective capacitance between points $A$ and $B$, when the space between the parallel plates of $C_1$ capacitor is filled with a dielectric medium having dielectric constant of 4, is :

Accepted Answer

Update Capacitance of $ C_1 $:
The initial capacitance of $ C_1 $ is $ 5 \, \mu 	ext{F} $. Adding a dielectric with a dielectric constant of 4 increases $ C_1 $ to:
$    C_1 = 4 	imes 5 = 20 \, \mu 	ext{F}    $
Identify Capacitances of $ C_2 $ and $ C_3 $:
Both $ C_2 $ and $ C_3 $ remain at $ 5 \, \mu 	ext{F} $ since no dielectric is added to them.
$    C_2 = 5 \, \mu 	ext{F}, \quad C_3 = 5 \, \mu 	ext{F}    $
Calculate Effective Capacitance:
Capacitors $ C_1 $ and $ C_2 $ are in series, and this series combination is parallel to $ C_3 $.
Series Combination of $ C_1 $ and $ C_2 $:
The formula for capacitors in series is:
$      C_{	ext{series}} = \frac{C_1 	imes C_2}{C_1 + C_2} = \frac{20 	imes 5}{20 + 5} = \frac{100}{25} = 4 \, \mu 	ext{F}      $
Parallel Combination with $ C_3 $:
The formula for capacitors in parallel is:
$      C_{	ext{eq}} = C_{	ext{series}} + C_3 = 4 + 5 = 9 \, \mu 	ext{F}      $
Thus, the effective capacitance between points $ A $ and $ B $ is $ 9 \, \mu 	ext{F} $.

Answer

$9 \mu \mathrm{~F}$

Answer

$30 \mu \mathrm{~F}$

Answer

$7.5 \mu \mathrm{~F}$

Answer

$22.5 \mu \mathrm{~F}$

Electrostatics & Capacitance

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