In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q₁ $$\mu$$C. Then S is switched to position Q. After a long time, the charge on the capacitor is q₂ $$\mu$$C.



The magnitude of q₁ is ________________.

In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q₁ $$\mu$$C. Then S is switched to position Q. After a long time, the charge on the capacitor is q₂ $$\mu$$C.



The magnitude of q₂ is ________________.

Two capacitors with capacitance values C₁ = 2000 $$ \pm $$ 10 pF and C₂ = 3000 $$ \pm $$ 15 pF are connected in series. The voltage applied across this combination is V = 5.00 $$ \pm $$ 0.02 V. The percentage error in the calculation of the energy stored in this combination of capacitors is ________.

A parallel plate capacitor of capacitance C has spacing d between two plates having area A. The region between the plates is filled with N dielectric layers, parallel to its plates, each with thickness, $$\delta = {d \over N}$$. The dielectric constant of the m^th layer is $${K_m} = K\left( {1 + {m \over N}} \right)$$. For a very large N(>10³), the capacitance C is $$\alpha \left( {{{K{\varepsilon _0}A} \over {d\ln 2}}} \right)$$

The value of $$\alpha $$ will be ..................

[$$ \in $$₀ is the permittivity of free space.]