Understanding electric current involves the movement of charges through a conductor, measured in Amperes. For a circuit to facilitate charge flow, it must be a closed loop, allowing uninterrupted passage from the power source. A potential difference drives the flow of current through the circuit.
Exploring the intricacies of electric current can be further pursued through the provided link. Meanwhile, essential formulas related to this topic can be explored below.
Formulas for Current Electricity
Electric Current
I = neAVd
Where n denotes the number of free electrons per unit volume, A is the cross-sectional area, e represents the charge of an electron, and Vd stands for drift velocity.
Current Density
j = i/A = σE
With i being the current, A the cross-sectional area, E the electric field, and σ symbolizing conductivity.
Drift Speed
Resistance of the Conductor
R = ρl/A, where ρ = 1/σ
Where ρ signifies resistivity and σ denotes conductivity.
Resistance and Temperature Relationship
R = R0(1 + αΔT)
R0 represents the initial resistance, R corresponds to the resistance at temperature T, and α signifies the temperature coefficient of resistance.
Ohm's Law
V = IR
Where V signifies voltage, I represents current, and R stands for resistance.
Kirchhoff's Laws
(i) Junction Law: ∑node Ii = 0.
(ii) Loop Law: ∑loop ΔVi = 0.
Resistance in Parallel
1/Req = 1/R1 + 1/R2
Resistance in Series
Req = R1 + R2
Wheatstone Bridge
Balanced Wheatstone bridge: P/Q = R/S
Electric Power
P = V2/R = I2R = IV
Galvanometer as an Ammeter
igG = (i – ig)S
Where G denotes galvanometer resistance, S represents shunt resistance, i signifies maximum current measured by the ammeter, and ig stands for the maximum current through the galvanometer.
Galvanometer as a Voltmeter
V = ig(R + G)
Where G stands for galvanometer resistance, ig represents maximum galvanometer deflection, and R symbolizes high resistance connected in series.
Charging of Capacitors
q(t) = CV(1 - e-t/RC)
Discharging of Capacitors
q(t) = q0e-t/RC
Time Constant in RC Circuit
τ = RC
Peltier Effect
(emf) = ΔH/ΔQ = Peltier heat/Charge transferred
Seebeck Effect
(i) Thermo-emf: e = aT + (1/2)bT2
(ii) Thermoelectric power: de/dt = a + bT
(iii) Neutral temperature: Tn = -a/b
(iv) Inversion temperature: Ti = -2a/b
Thomson Effect
emf e = ΔH/ΔQ = Thomson heat/Charge transferred = σΔT
Faraday's Law of Electrolysis
m = Zit = (1/F)Eit
Where i denotes current, t is time, Z signifies electrochemical equivalent, E represents chemical equivalent, and F stands for Faraday constant (96485 C/g).
Current and electricity concepts form a significant portion of the JEE syllabus, and mastering these formulas can greatly enhance your problem-solving skills in this subject. The above formulas cover the basic principles of current, power, energy, and key concepts related to electrical components. As you prepare for the JEE, make sure to practice applying these formulas to a variety of problems. A strong grasp of these concepts will not only help you succeed in the exam but also lay a solid foundation for your future endeavors in the field of electrical and electronic engineering.
Important Current And Electricity Formulas FAQs
Q1. What are Kirchhoff's Laws?
Ans. Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) are used to analyze complex circuits.
Q2. How is energy (E) consumed by a device calculated?
Ans. Energy E is calculated as E=P⋅t, where P is power and t is time.
Q3. What is Ohm's Law?
Ans. Ohm's Law states that voltage (V) is directly proportional to current (I) and inversely proportional to resistance (R): V=I⋅R.
Q4. How is power (P) calculated in terms of current and voltage?
Ans. Power P is given by P=I⋅V.