ALTERNATING CURRENTS
AC or alternating emf values vary periodically w/ time in magnitude & direction

1 complete alternation = 1 cycle
# of cycles in a second = freq
sine curve AC; ξ = ξ₀sinωt

Power in a resistance circuit
av. I / emf of AC = 0 (for complete cycle)

rms (root mean square) / effective value of AC = steady I (DC) which produces same heating effect as the AC in a given R

sinusoidal AC: I = I₀sinωt = I₀sin2πft
P = I_DC²R = (mean of I_AC²) × R
I_DC² = mean of I_AC² => I_DC = √(mean of I_AC²) = I_rms
I_rms = √(mean of I₀²sin²ωωt) = I₀√(mean of sin²ωt)

from graph: mean of sin²ωt = ½
I_rms = I₀√(½) = I₀/√2 = 0.707 I₀

mean P of R = ½P_max of AC (P = I²R = I_rms²R = ½I₀²R)
Simple transformers

-consists of 2 coil wound onto Fe core
-used to change voltages
AC supply => changing mag flux in Fe core => V_induced on secondary coil
ideal: V_S/V_P = N_S/N_P
P_input = P_output => I_PV_P = I_SV_S
V_S/V_P = N_S/N_P = I_P/I_S

electricity transmitted over long dist > R in cables > energy loss
min E loss: high V, low I => substation step-up V (to 220000V) before transmission => step-down before used (240V)
high V: more efficient but dangerous => needs good insulation

Rectification of AC (AC > DC)
rectifier (diode) : low R in 1 direction (forward direction, forward bias), high R in other direction (reverse direction, reverse bias)
Half wave rectification


1st half cycle: forward dirⁿ => I pulses in output (pd_out pd_input, slight R)
2nd half cycle: reverse dirⁿ => v.little/ no I pulses in output
I unidirectional => pd_out direct (only fluctuates, doesn't change dirⁿ)
Full wave rectification


4 diodes arranged in bridge network
A: +ve => 1,2 conduct (D > B doesn't occur as potential at D is less than potential at B)
(ABC > pd_out > DEF)
A: -ve => 3,4 conduct (FEC > pd_out > DBA)
both halves of pd_input converted to pd_out in same dirⁿ

I_out unidirectional, but pd_out varies from max to 0
to obtain more steady DC output, use smoothing circuit
Smoothing circuit


-use reservoir capacitor (large capacitor, >= 10µF)
OA: capacitor charged to almost peak V while V_R ^ to peak V
at A: input pd decreases below V_C => capacitor discharges through load (not through rectified pd as wrong polarity)
at B: input pd = value V₁ has fallen to => capacitor quickly charged, V_R ^ to peak => cycle repeats

larger capacitor => better smoothing (V_R falls less) but initially uncharged capacitor acts like a short circuit => I surge => can damage rectifier


Back to 'A' level notes index

Back to notes index