Question

Two capacitors of capacitance 200pf and 600pf connected in parallel and then charged to the potential 120v .then the value of the total charge on the capacitor is

Answer 1

$\boxed{ \red{ \underline{ \purple{ \mid} \overline{ \sf \green{Answer}} \purple{\mid} }} } : - \\ \leadsto \boxed{ \sf{ q = 96 \times {10}^{ - 9} \: coulamb \: }} \\ \bf{ or \: } \\ \leadsto \boxed{ \sf{q=9.6\times{10}^{ - 8}\: coulamb\:}}\:\\ \\\boxed{\red{\underline{ \purple{ \mid} \overline{\sf{\orange{To \: Find}}} \purple{\mid} }}} : \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ - Total \: charge \: on \: capacitor .} \: \\ \boxed{ \red{ \underline{ \purple{ \mid} \overline{ \sf \pink{Explan} \green{ation}} \purple{\mid} }} } : - \: \\ \\ \green{ \bf{Given}\begin{cases}\sf{\red{C_{1} \: =200 \: }p \: f }\\\sf{\blue{C_{2} = 600 \:p}\:f}\\\sf{\pink{potential(V)} = 120 \: v}\end{cases}}</p><p> \:$

Given both capacitors are in parallel combination hence equivalent capacitor (C) is

$\red{\implies } \sf{\: C = C_{1} + C_{2} \: } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{= 200 \: p \: f + 600 \: p \: f} \\ \: \: \: \: \: \: \: \: \: \: \: \: \sf{C = \red{ 800 \: p \: f \: }}$

And , we know that

$\implies \boxed{ \sf{C \: = \green{ \frac{Total \: charge (q)}{v} }}} \\ \\ \leadsto \sf{800 \: p \: f = \red{\frac{q}{120} } } \\ \\ \leadsto \sf{ q = \pink{800 \: p \: f \times 120 \: } }\\ \\ \leadsto \sf{ q = 800 \times {10}^{ - 12} \times 120} \: \: \\ \\ \because \boxed{\sf{ \: 1 \: pico(p) \: \green{ farad\: = {10}^{ - 12} } \: farad \: }} \\ \\ \leadsto \boxed{ \sf{ q = \orange{96 \times {10}^{ - 9} \: coulamb }\: }} \\ \bf{ or \: } \\ \leadsto \boxed{ \sf{q = \red{ 9.6 \times {10}^{ - 8} \: coulamb \: }}}$

Answer 2

★ GiveN :

First Capacitor ($\sf{{C_1})}$ = 200pf

Second Capacitor ($\sf{{C_2})}$ = 600pf

Both capacitors are in parallel combination.

Potential (v) = 120 v

$\rule{200}{1}$

★ To FinD :

We have to find total charge on capacitor (Q).

$\rule{200}{1}$

★ SolutioN :

As, both the capacitors are in parallel combination.

So,

$\Large{\implies{\boxed{\boxed{\sf{C = C_1 + C_2}}}}}$

Where,

• C is equivalent capacitor.

★ Putting Values ★

$\sf{\dashrightarrow C = 200pf + 600 pf} \\ \\ \sf{\dashrightarrow C = 800pf} \\ \\ \Large{\implies{\boxed{\boxed{\sf{C = 800pf }}}}}$

$\rule{150}{2}$

Now,

$\Large{\implies{\boxed{\boxed{\sf{C = \frac{Q}{v}}}}}}$

★ Putting Values ★

$\sf{\dashrightarrow 800pf = \frac{Q}{120}} \\ \\ \bf{\dag \: \: \: By \: Cross \:Multiplication.} \\ \\ \sf{\dashrightarrow Q = 800pf \times 120} \\ \\ \Large{\star{\boxed{\sf{1 \: pf = 10^{-12}}}}} \\ \\ \sf{\dashrightarrow Q = 800 \times 10^{-12} \times 120} \\ \\ \sf{\dashrightarrow Q = 96000 \times 10^{-12}} \\ \\ \sf{\dashrightarrow Q = 96 \times 10^{-9}} \\ \\ \Large{\implies{\boxed{\boxed{\sf{Q = 96 \times 10^{-9}}}}}}$

$\therefore$ Total charge on Capacitors is $\sf{96 \times 10^{-9}}$.