Alternating Current

Alternating Currents

Characteristics of alternating currents

Peak current, I₀ = 3 A

Peak-to-peak current, I_p-p = 6 A

Period, T = 20 ms

Frequency, f = 1 / T = 50 Hz

Angular Frequency, ω = 2 π f = 314 rad s^-1

Instantaneous current: the current at a particular instant.

Since this A.C. signal can be described by the equation:

I = I0 sin (ω t)
or V = V0 sin (ω t)
the instantaneous current I or voltage V at time t is given by I₀ sin (ωt) or V₀ sin (ωt).

Note: Both the period and amplitude of a sinusoidal A.C should be constant.

Root-mean-square current of an alternating current is defined as that steady {NOT direct} current that produces the same heating effect {ie I² R} as the alternating current in a given resistor.

(Instantaneous) sinusoidal current: I = I₀sinωt , { Similarly, V = V₀ sinωt }

I_rms = I_o / √2, V_rms = v_o / √2, {for sinusoidal ac only}

Relationship between Peak, & RMS values of PD & Current: V₀ = I₀R , V_rms = I_rmsR

Mean/Ave Power, P_ave = I_rms² R = V_rms² / R = I_rms / V_rms = ½ x Maximum Instantaneous Power = ½ I₀V₀ {for sinusoidal AC}

Max (Instantaneous) Power, P_max = I₀V₀ = I₀² R

The root-mean-square (R.M.S.) value, I_rms, of an A.C. is the magnitude of the direct current that produces the sameaverage heating effect as the alternating current in a given resistance whereas peak value is the maximum current of an AC.

Ideal transformer: V_p I_p = V_s I_s → N_S / N_P = V_S / V_P = I_P / I_S

{Mean power in the primary coil = Mean power in the secondary coil )

{Values of I & V may be either R.M.S. or peak but not instantaneous values; N_S / N_P: turns ratio}

Power Loss during Transmission of Electrical Power

Power Generated at power station P_gen = V_i I,
where I: current in the transmission, Vi: Voltage at which power is transmitted

I = P_gen / V_i

Power Loss in Transmission Cables, P_L = I² R_C = (P_gen / V_i)² R_C ;R_C = cable resistance

Thus to reduce power loss, for a given amt of power generated, electricity is transmitted at high voltage V_i {ie low current}. {V_iis NOT the pd across the cables}

Rectification with a diode

If a single diode is connected to an A.C. circuit as shown, a half-wave rectification occurs.

The graphs for the input and output voltages, and the output current, are shown below.

In the regions A and C, the diode is forward biased, allowing current to flow. When the input voltage becomes negative, the diode prevents the current flow, because it is reverse biased.