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Key Equations

Mutual inductance by flux M=N2Φ21I1=N1Φ12I2M=N2Φ21I1=N1Φ12I2
Mutual inductance in circuits ε1=MdI2dtε1=MdI2dt
Self-inductance in terms of magnetic flux NΦm=LINΦm=LI
Self-inductance in terms of emf ε=LdIdtε=LdIdt
Self-inductance of a solenoid Lsolenoid=μ0N2AlLsolenoid=μ0N2Al
Self-inductance of a toroid Ltoroid=μ0N2h2πlnR2R1.Ltoroid=μ0N2h2πlnR2R1.
Energy stored in an inductor U=12LI2U=12LI2
Current as a function of time for a RL circuit I(t)=εR(1et/τL)I(t)=εR(1et/τL)
Time constant for a RL circuit τL=L/RτL=L/R
Charge oscillation in LC circuits q(t)=q0cos(ωt+ϕ)q(t)=q0cos(ωt+ϕ)
Angular frequency in LC circuits ω=1LCω=1LC
Current oscillations in LC circuits i(t)=ωq0sin(ωt+ϕ)i(t)=ωq0sin(ωt+ϕ)
Charge as a function of time in RLC circuit q(t)=q0eRt/2Lcos(ωt+ϕ)q(t)=q0eRt/2Lcos(ωt+ϕ)
Angular frequency in RLC circuit ω=1LC(R2L)2ω=1LC(R2L)2
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