University Physics Volume 2

# Key Equations

### 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 $I(t)=εR(1−e−t/τL)I(t)=εR(1−e−t/τL)$ 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 $q(t)=q0e−Rt/2Lcos(ω′t+ϕ)q(t)=q0e−Rt/2Lcos(ω′t+ϕ)$ Angular frequency in RLC circuit $ω′=1LC−(R2L)2ω′=1LC−(R2L)2$