If you are looking for help on the Concept of Capacitance you have come the right way. After going through this page you can have an idea on Capacitance Formulas and can solve various questions related to them. Check out the Formulas on Capacitance such as Capacitance of Conductor, Capacitance of Spherical Conductor, Parallel Plate Capacitor, etc.

Make the most out of the **Physics Formulas** for several concepts and master the relevant topics easily. Just access the relevant Capacitance Cheat Sheet while solving concerned problems and apply them to get results easily.

**1. Capacitance of a conductor**

Capacity of storing charge

C = \(\frac{Q}{V}\)

Unit → farad = \(\frac{\text { coulomb }}{\text { volt }}\)

**2. Capacitance of a spherical conductor**

C = 4πε_{0}R

R → Radius of conductor.

**3. Common potential when two charged conductors are connected**

C = C_{1} + C_{2}

Q = Q_{1} + Q_{2} = C_{1}V_{1} + C_{2} V_{2}

Common potential

V = \(\frac{\mathrm{C}_{1} \mathrm{V}_{1}+\mathrm{C}_{2} \mathrm{V}_{2}}{\mathrm{C}_{1}+\mathrm{C}_{2}}\)

Charge transferred

ΔQ = \(\frac{C_{1} C_{2}}{C_{1}+C_{2}}\) (V_{1} – V_{2})

Energy loss

ΔU = \(\frac{1}{2} \frac{C_{1} C_{2}}{C_{1}+C_{2}}\) (V_{1} – V_{2})^{2}

**4. Capacitor (condenser)**

An arrangement of conductors for increasing the capacitance. It has two conductors placed nearby, one is charged and the other is earthed.

**5. Parallel plate capacitor**

C = \(\frac{\epsilon_{0} A}{d}\), C_{m} = ε_{r} = \(\left(\frac{\epsilon_{0} A}{d}\right)\) = ε_{r}C

If a dielectric of thickness t is placed in between, then

C = \(\frac{\epsilon_{0} A}{\left(d-t+\frac{t}{\epsilon_{r}}\right)}\)

(a)

If slabs of thickness t_{1}, t_{2}, t_{3} …. t_{n} of dielectric constant’s ε_{r1}, ε_{r2}, …… ε_{rn} are placed in between

C = \(\frac{\epsilon_{0} A}{\left(\frac{t_{1}}{\epsilon_{r_{1}}}+\frac{t_{2}}{\epsilon_{r_{2}}}+\ldots .+\frac{t_{n}}{\epsilon_{r_{n}}}\right)}\)

and d = t_{1} + t_{2} + t_{3} + …. + t_{n}

(b)

**6. Spherical capacitor**

When outer spherical shell is earthed

C = 4πε_{0}ε_{r} \(\frac{\mathrm{R}_{1} \mathrm{R}_{2}}{\mathrm{R}_{2}-\mathrm{R}_{1}}\) ; R_{2} > R_{1}

When inner sphere is earthed

C = 4πε_{0}ε_{r} \(\frac{\mathrm{R}_{1} \mathrm{R}_{2}}{\mathrm{R}_{2}-\mathrm{R}_{1}}\) + 4πε_{0}R_{2}

**7. Cylinderical condenser**

C = \(\frac{2 \pi \epsilon_{0} \epsilon_{\mathrm{r}} \ell}{\log _{\mathrm{c}}\left(\mathrm{R}_{2} / \mathrm{R}_{1}\right)}\)

**8. Capacitance of a two wire line**

C = \(\frac{\pi \epsilon_{0} \epsilon_{1} \ell}{\log _{e}(d / r)}\) (d >> r)

l → length of each wire

d → distance between wires

r → radius of each wires

**9. Multiplate capacitor**

C = (n – 1) \(\frac{\epsilon_{0} \in_{r} A}{d}\)

A → area of each plate.

**10. Energy stored in a capacitor**

U = \(\frac{1}{2}\) CV^{2} = \(\frac{1}{2}\) QV = \(\frac{1}{2} \frac{Q^{2}}{C}\)

This energy resides in electric field. Energy density of electric field

U = \(\frac{1}{2}\) εE^{2} = \(\frac{\text { Total Energy }}{\text { Volume }}\)

**11. Combination of capacitor**

Series combination

\(\frac{1}{C}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\ldots \ldots+\frac{1}{C_{n}}\)

Q_{1} = Q_{2} = …….. = Q

V = V_{1} + V_{2} + V_{3}+ ……… + V_{n}

Parallel combination

C = C_{1} + C_{2} + …….. C_{n}

V_{1} = V_{2} = …….. = V

Q = Q_{1} + Q_{2} + Q_{3} + …….. + Q_{n}

**12. Charging and discharging of a capacitor through a resistance**

Charging

q = q_{0} (1 – e^{-t/RC})

V = V_{0} (1 – e^{-t/RC})

I = I_{0} e^{-t/RC}, I_{0} = \(\frac{V_{0}}{R}\)

V → P.d. across capacitor

q → charge on the capacitor

I → current through the capacitor

Discharging

q = q_{0} e^{-t/RC}

V = V_{0} e^{-t/RC}

I = – I_{0} e^{-t/RC}

Time constant

while charging

τ = RC, time in which q = 0.63Q, V = 0.63V_{0} and I = 0.37I_{0}

while discharging q = 0.37Q, V = 0.37V_{0} and I = 0.37I_{0}

- In charging energy supplied by the battery up to steady state is V
_{0}q_{0} - Energy stored in capacitor as a electric field is \(\frac{1}{2}\)V
_{0}q_{0} - Energy loss during charges = \(\frac{1}{2}\) V
_{0}q_{0}

**13. Force of attraction between the plates of a capacitor**

F = \(\frac{1}{2}\) εE^{2} A = \(\frac{Q^{2}}{2 \in A}=\frac{1}{2} \frac{C V^{2}}{d}\)

F = \(\frac{\sigma^{2}}{2 \epsilon}\)A

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