Relationships in the RL Circuit

resister and inductor in a series connection. In the circuit, current flows through the inductor and resistance.

let current flow i in the circuit, and the potential difference resistance and inductor are V_R and V_L.

So potential across the resistance:

V_R(t)=(Vo)_rsin(ωt)

and inductor-

V_L(t)=(Vo)_LRsin(ωt+π/2) :: (where π/2 is the voltage lead current)

So, resultant potential:

V_o=√(V_o)²_r+(V_o)_L²

=√(I_oR²)+(IoX_l)²

V_o=I_o √R²+X_L² where Z=impedence of RL circuit=√R²+X_L²

Then V_o = IoZ, where_o Io is the _o current in amps.

Instantaneous current and voltage in an RL circuit

i=E/R(1-ϵ^-tR/L)

Where i = instantaneous current in amperes at time t

E = supply voltage

R = series resistance, in ohms (including inductor winding resistance)

ε = exponential constant =2.718

t = time in seconds from current start

L =represents the inductance of the inductor, measured in Henry.

Frequency Response

The frequency response of an RL (resistor-inductor) circuit can be expressed in terms of impedance.

Z=√R²+(2*pai*f*L)² where f=frequency in Ac signal

Phase Difference

[Tex]tan(\phi) [/Tex]=X_L/R

Power in RL Series Circuit

Alternating Voltage across the circuit is given as

[Tex]v=V_msin\omega t [/Tex]

Current can be given as

[Tex]i=I_msin(\omega t-\phi) [/Tex]

so ,the instantaneous power is given by the Equation

p=v i

now Substituting the value of v and I from the above equation,

[Tex]P=(V_m sin\omega t)* I_m sin(\omega t-\phi) [/Tex]

[Tex]p=\frac{V_mI_m}{2}*2sin(\omega t – \phi)sin\omega t [/Tex]

[Tex]p=\frac{V_m}{\sqrt{2}}*\frac{I_m}{\sqrt{2}}[cos\phi -cos(2\omega t – \phi)] [/Tex]

[Tex]\frac{V_m}{\sqrt{2}}*\frac{I_m}{\sqrt{2}} cos\phi-\frac{V_m}{\sqrt{2}}*\frac{I_m}{\sqrt{2}}cos(2\omega t-\phi) [/Tex]

so the average power consumed in one cycle in the circuit can be given by

[Tex]p= average of \frac{V_m}{\sqrt{2}}*\frac{I_m}{\sqrt{2}} cos\phi- average of\frac{V_m}{\sqrt{2}}*\frac{I_m}{\sqrt{2}}cos(2\omega t-\phi) [/Tex]

so p can be calculated as

[Tex]p=V_(rms)*I_(rms)cos\phi = VI cos\phi [/Tex]

where [Tex]cos\phi [/Tex] is the power factor

[Tex]cos\phi [/Tex] can be calculated as

[Tex]cos\phi=\frac{V_R}{V}=\frac{IR}{IZ}=\frac{R}{Z} [/Tex]

Now substituting this Value we will get

[Tex]P=IZ*I*\frac{R}{Z}=I^{2}*R [/Tex]

Power Consume in the Circuit is [Tex]I^{2}*R [/Tex]

Time Constant Formula

T=L/R

Inductor current doesn’t change instantaneously So transit responses are measured in terms of the ratio of the inductor and resistance.

[Tex]\Tau=L/R [/Tex] where L is inductor and R is resistance

Waveform and Power Curve of the RL Series Circuit

The Following Represents the Wave Form and power Curve of the RL Circuit. The power is positive in the Cycle Except between angle 0 and [Tex]\phi [/Tex] and during180 and [Tex](180+\phi) [/Tex].

In this Article, we will see the characteristics of circuits consisting of a resistor and an inductor in series (RL circuits). The primary focus will be on the response of an RL circuit to a step voltage and a voltage square wave. An RL circuit, also referred to as a resistor-inductor circuit, plays a foundational role in electrical engineering and inductive elements.

In this Article, We will be going through the RL Circuit, We First go through What is the RL Circuit, and We will see RL circuit formulas, Waveforms, and Power curves. At last, we will conclude our Article with its Advantages, Disadvantages, and Some FAQs.