Current electricity Formulas - Physics Formula
1. Electric Current(i)
`i_{avg}=\frac{\triangle q}{\triangle t}`
`i_{ins}=\frac{dq}{dt}`
Current has both magnitude and direction but still it's a Scalar quantity because it does not follow vector law of addition.
2. Drift velocity
`v_d=\frac{eE\tau}{m_e}`
`a=\frac{eE}{m_e}`
`\lambda=\frac{eE\tau^2}{2m_e}`
3. Relation between i and `v_d`
`i=nAev_d`
4. Ohm's law
V=IR
`R=\frac VI=\frac{ml}{nAe^2\tau}`
`R=\frac{\rho l}A`
5. If Length of Resistor is L, It is stretched so that final length become 'nL'. So new resistance will be
`R'=R_0n^2`
6. Effect of Temperature on Resistance / Resistivity
`R=R_0(1+\alpha\triangle T)`
`\rho=\rho_0(1+\alpha\triangle T)`
For conductors: `\alpha`= positive
For semiconductor:`\alpha`=negative
For Alloys:`\alpha`=Zero (almost zero)
7. Colour coding of carbon resistor
Trick:" BB ROY of Great Britain has a Very Good Wife who wear Gold Silver Nacklace"
B : 0
B : 1
R : 2
O : 3
Y : 4
G : 5
B : 6
V : 7
G : 8
W : 9
G : 5%
S : 10%
NC : 20%
8. Current Density
`J=\frac iA`
9. Ohm's law vector form
`E=J\rho`
Where E= Electric field
J= Current density
`rho`= Resistivity
10. Series Combination of Resistors
`R_{eq}=R_1+R_2+...`
`V_1:V_2=R_1:R_2`
11. Parallel Combination of Resistors
`\frac1{R_{eq}}=\frac1{R_1}+\frac1{R_2}+...`
`i_1:i_2=\frac1{R_1}:\frac1{R_2}`
12. Cell, EMF
`V=\varepsilon-iR`
13. Kirchoff's Rule
First Law : Based on conservation of charge
Second Law: Based on conservation of Energy
14. Combination of Cells
Series Combination
`\varepsilon_{eq}=\varepsilon_1+\varepsilon_2+..`
`r_{eq}=r_1+r_2+...`
Parallel Combination
`\varepsilon_{eq}=\frac{{\frac{\varepsilon_1}{r_1}}+{\frac{\varepsilon_2}{r_2}}}{{\frac1{r_1}}+{\frac1{r_2}}}`
15. Electric Power and Energy
`E_{cell}=W_{cell}=qV`
`P=VI=I^2R=\frac{V^2}R`
Energy`=i^2Rt=\frac{V^2R}t=Vit`
16. Bulb
Brightness is directly proportional to Power.
`P=i^2R=\frac{V^2}R`
17. Meter Bridge
`\frac{R_1}l=\frac{R_2}{100-l}`
When l=50cm, value will be most accurate (error will be minimum)
18. Potentiometer
Potential Gradient (K)
`K=\frac VL`
`E=\frac{Vx}l`
Comparing EMF of 2 cells
`\frac{E_1}{E_2}=\frac{x_1}{x_2}`
Finding internal resistance of a cell
`r=R\left(\frac{l_1}{l_2}-1\right)`
19. Galvanometer
Concert into Ammeter
`I_gG=(I-I_g)S`
Concert into Voltmeter
`V=I_g(G+R)`
20. Electron Mobility
`\mu_e=\frac{v_d}E`
Where `V_d` is Drift velocity
And E is Electric Field.
21. Maximum Power Theorem
Power is maximum when internal resistance is equal to external resistance.
r=R
22. When a current is Flowing in a wire, the wire itself is electrically neutral.