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# Circuits

By Levi Clancy for Student Reader on
updated

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Magnetic field of a loop of wire: B = µ0 I / 2 R

Capacitor

Time rate of electric field on a capacitor: dE/dt = I / ( ε0 A )
(where A is the area of a capacitor plate)

Electric field between capacitor with a charge: E = Q / ( ε0 A )

Concepts

For positive charges, F and E are opposite.

For negative charges, F and E are the same direction.

Potential energy between two charges: U = k q1 q2 / r122

Θ = qenclosed / ε0

For an infinite line: qenclosed = λ L and E = 2 k λ / r

For a sheet: E = ½ σ / ε0

For two plates: E = - V / d (ΔV between plates, divided by distance between plates)

For a circle: E = k q / r2

Coils

Cylindrical air coil: L (inductance) = µ0 N2 A / l

Circuit

ΔV = I R = E d

ΔU = q ΔV for some test charge

Q = C V = ε0 A E

W = ΔU = - q ΔV

ΔV = ΔU / q = k q / r

℘ = I2 R = I ΔV = ΔV2 / R = I Ε

Ε = I R + I r (way to find epsilon when an external resistor is in the circuit)

R is external resistance, r is internal battery resistance

ΔV = Ε - I r

I = Ε / ( R + r)

Epsilon is EMF, the Delta V when no resistor is in place if you will, and delta V is the voltage difference when the resistor is connected.

 Series Parallel Diff ΔV Same ΔV Same Q Different Q Ctotal-1 = C1-1 + C2-1 Ctotal = C1 + C2 Vtotal = V1 + V2 V1 = V2 Rtotal = R1 + R2 Rtotal-1 = R1-1 + R2-1 Itotal = I1 = I2 I1 = Itotal ( Rtotal - R1 ) / Rtotal