In the given circuit. $$C_1 = 2\mu F$$, $$C_2 = 0.2\mu F$$, $$C_3 = 2\mu F$$, $$C_4 = 4\mu F$$, $$C_5 = 2\mu F$$, $$C_6 = 2\mu F$$. The charge stored on capacitor $$C_4$$ is _______ $$\mu$$C.

Given:

C1=2,  C2=0.2,  C3=2,  C4=4,  C5=2,  C6=2 μFC

Battery:

10V

Need charge on $$C_4$$​.

Let top-left node be 10V, bottom-left be 0V.

Let central top node = $$V_a$$

central bottom node = $$V_b$$

top-right node = $$V_c$$

bottom-right node = $$V_d$$

For floating nodes, net charge = 0.

At $$V_a$$:

$$2(V_a-10)+0.2(V_a-V_b)+2(V_a-V_c)=0$$

$$4.2V_a-0.2V_b-2V_c=20$$

At $$V_b$$​:

$$2(V_b-0)+0.2(V_b-V_a)+2(V_b-V_d)=0$$

$$-0.2V_a+4.2V_b-2V_d=0$$

At $$V_c$$​:

$$2(V_c-V_a)+4(V_c-V_d)=0$$

$$-2V_a+6V_c-4V_d=0$$

At $$V_d$$​:

$$2(V_d-V_b)+4(V_d-V_c)=0$$

$$-2V_b-4V_c+6V_d=0$$

Solving gives

$$V_c-V_d=1V$$

Charge on $$C_4$$:

$$Q_4=C_4(V_c-V_d)$$

$$=4\times1=4$$