Some Important Formulas [Electrical] 
Ohm's Law for D.C. Circuits 
P = 
EI = 
I^{2}R = 
E^{2} 
watts 
R 
I = 
E 
= 
P 
= 
√P/R = 
Ampere 
R 
E 
R = 
E 
= 
E^{2} 
= 
P 
= 
Ohm's 
I 
P 
I^{2} 

▷ Resistors in series = R = R_{1} + R_{2} + R_{3} +... R_{n} 
▷ Resistors in parallel = 
1 
= 
1 
+ 
1 
+ 
1 
+... 
1 
R 
R_{1} 
R_{2} 
R_{3} 
R_{n} 

Capacitors & Electrostatics 
▷ Capacitors in parallel = C = C_{1} + C_{2} + C_{3} +... C_{n} 
▷ Capacitors in series = 
1 
= 
1 
+ 
1 
+ 
1 
+... 
1 
C 
C_{1} 
C_{2} 
C_{3} 
C_{n} 
▷ Capacitance of capacitor C = 
Q 
V 
▷ Energy stored in capacitor W = 
1 
CV^{2} 
2 
▷ Coulomb's law F = 
Q_{1} Q_{2} 
4πԐ_{0}Ԑ_{r} r^{2} 
▷ Electric field strength E = 
Q 
4πԐ_{0}Ԑ_{r} r^{2} 
▷ Electric flux density D = 
Q 
4πr^{2} 
▷ Electric potential at a point due to point charge q: V = 
q 
4πԐ_{0}Ԑ_{r} r 
▷ Potential due to number of charges V = 
1 
[ 
q_{1} 
+ 
q_{2} 
+... 
] 
4πԐ_{0}Ԑ_{r} 
r_{1} 
r_{2} 
▷ Charging of capacitor i = 
V 
e^{t/RC} 
R 
▷ Discharging of capacitor i = 
V 
e^{t/RC} 
R 

Electromagnetic Induction, Magnetic circuit, Inductance 
▷ Faraday's law electromagnetic induction e = N 
dΦ 
dt 
▷ Dynamically induced emf = B l v Sinθ 
▷ Self induced emf = L 
di 
dt 
▷ Mutual induced emf = M 
di_{1} 
dt 
▷ Self inductance L = 
NΦ 
l 
▷ Mutual inductance M = 
N_{2} Φ_{2} 
l_{1} 
▷ Coefficient of coupling k = 
M 
√L_{x}L_{y} 
▷ Time constant for RL circuit T = 
L 
R 
▷ Energy stored in magnetic field = 
1 
L I^{2} 
2 
▷ Magnetomotive force mmf = NI 
▷ Magnetic field strength H = 
NI 
l 
▷ Reluctance H = 
l 
µ_{0}µ_{r} a 
▷ Ohm's law for magnetic circuit mmf = flux X reluctance 
▷ Hysteresis loss P_{h} = ηV.f(B_{max})^{1.6} 
▷ Eddy current loss P_{e} = k.(B_{max})^{2}f^{2}t^{2}V [note here V is volume not voltage] 
▷ Ampere turn for iron parts AT_{i} = 
B_{i} 
.l_{i} = H_{i}l_{i} 
H_{i} 
▷ Ampere turn for air gap AT_{g} = 0.796 B_{g}l_{g} X 10^{6} 
▷ Leakage factor = 
Φ_{T} 
Φ 
▷ Force experienced by conductor F = BIlsinθ 
▷ Magnetic field due to an infinite linear conductor H = 
1 
2πr 
▷ Flux density due to circular loop B_{z} = 
μIR^{2} 
2(R^{2} + Z^{2})^{3/2} 
▷ Flux density at the centre of solinoid B_{c} = 
μNI 
√4R^{2} + I^{2} 
▷ Force between two parallel conductors F = 
μ_{0} I I^{'} 
.I 
2πr 
▷ Magnetic Flux density B = 
Φ 
A 
▷ Ampere's circuit law ∫H dl = ∑ I 
▷ Biotsavart's law dH = 
I 

Idl 
sinθ 
4π 
r^{2} 

▷ For extension of range of ammeter, shunt resistance R_{sh} is given by: 
R_{sh} = R_{m}/(m1) 
▷ For extension of range of voltmeter, series resistance R_{s} is given by: 
R_{s} = (m1)R_{m} 
▷ The unknown resistance R_{s} to be measured by wheatstone bridge method is: 
R = (P/Q)S 

▷ RL series circuit ν = V_{max}Sin ax 
i = I_{max}Sin (ax  Φ) 
rms value of current = I = V/Z 
where Z = √R^{2} + X^{2}_{L} 
In inductive circuit, the current lag the applied voltage by an angle Φ 
▷ RC series circuit ν = V_{max}Sin ax 
i = I_{max}Sin (ax + Φ) 
rms value of current = I = V/Z 
where Z = √R^{2} + X^{2}_{C} 
In capacitive circuit, the current leads the applied voltage by an angle Φ 
▷ RLC series circuit Z = √R^{2} +
(X_{L}  X_{C})^{2} 
▷ Active power = V I CosΦ 
▷ Apparant power = V I 
▷ Reactive power = V I SinΦ 
▷ Power factor CosΦ = 
Active power 
= 
R 
Apparant power 
Z 
▷ Resonance in RLC circuit occurs at a frequency given by f_{r} = 
1 
2π√LC 
▷ At resonance X_{L} = X_{C} 
Impedance is minimum 
Current is maximum 
Power factor is unity 

▷ For ideal transformer I_{p}N_{p} = I_{s}N_{s} ;
V_{p}I_{p} = V_{s}I_{s} 
Transformer ratio k = 
E_{p} 
= 
V_{p} 
= 
N_{p} 
= 
I_{s} 
E_{s} 
V_{s} 
N_{s} 
I_{p} 
Only current I is secondary/primary here 

▷ Synchronous speed of rotating magnetic field, N_{s} = 
120 X f 
P 
▷ Percentage slip, S = 
N_{s}  N 
N_{s} 

▷ For 3 phase star connection with balanced load 
I_{L} = I_{ph} 
V_{L} = √3 X V_{ph} 
P = √3 V_{L}I_{L}CosΦ 
▷ For 3 phase delta connection with balanced load 
I_{L} = √3 I_{ph} 
V_{L} = V_{ph} 
P = √3 V_{L}I_{L}CosΦ 

▷ EMF of a DC Machine, E_{g} = 
PΦI_{a}Z 
A 
▷ Constant losses = Iron losses + Mechanical losses 

Keep visiting this article daily for more detail [under construction] 
