Current Electricity
CURRENT ELECTRICITY
Current electricity is the rate of flow of charge through any cross-section of a wire. Current electricity allows the flow of current from one place to another. There is a constant flow of charged particles such as electrons or ions in current electricity. Current electricity forms the basis for powering up any kind of electrical and electronic device. The formula of electric current is: I =q/t. The SI unit of Electric current is Ampere. The conventional direction of electric current is the direction of motion of the positive charge.
What is Electric Current?
The electric current is the same for all cross-sections of a conductor of a non-uniform cross-section. The current flows due to the motion of free electrons in a metallic conductor. In electrolytes and ionized gases, current flows due to the motion of electrons and positive ions. If a charge q revolves in a circle with frequency f, the equivalent electric current is,
Types of Electric current
As per the magnitude and direction of electric current it is of two types i.e,
- Direct Current
- Alternating Current
In Direct current, its magnitude and direction do not change with time. Its sources are battery, cell, or DC dynamo. In Alternating current, its magnitude changes continuously and direction periodically. Its source is AC dynamo.
Current Density
Current Density refers to the electric current flowing per unit area of a cross-section of a conductor. Its formulae are J = I/A. Its SI unit is Ampere metre2. It is a vector quantity and it is in the direction of motion positive charge or flow of current.
Thermal Velocity of Free Electrons
When free electrons in a metal move randomly with a very high speed of the order of 105 ms-1. The average thermal velocity of free electrons in any direction remains zero.
Drift Velocity of Free Electrons
When a potential difference is applied across the ends of a conductor, the free electrons in it move with an average velocity opposite to the direction of the electric field. The relationship between the electric current and drift velocity is Vd = I/An e.
Mobility
The Drift Velocity of an electron per unit electric field applied. The formula is Vd/E. Its SI unit is m2s-1v-1
Ohm’s Law
- Ohm’s law states that the electric current flowing through the conductor is directly proportional to the potential difference (V) applied across its ends.
- It is written as V=IR where R is the electrical resistance of a conductor.
- Ohm’s law gives the relationship between electric current and potential difference.
- Ohm’s law holds only if provided temperature and physical factors remain constant.
- In filament of the light bulb, increasing the current raises the temperature and thus Ohm’s law cannot be applied.
Water Pipe Analogy
Ohm’s law describes current flow through a resistance when different voltages are applied at each end of resistance. It's not possible to see the electrons, therefore the water pipe analogy helps us understand electric circuits in a better way. This analogy is a good mechanical system ie analogous to an electric circuit. Here Voltage is analogous to water pressure, the current is the amount of water flowing through the pipe and resistance is the size of the pipe. More water will flow through a pipe (current) when more pressure is applied (voltage) and bigger is the pipe (low resistance).
Water Pipe Analogy
Calculating Electrical Power using Ohm’s Law
- The rate at which energy is converted from electrical energy of moving charges to other forms like mechanical energy, heat, magnetic fields in electric fields is known as Electric power.
- The unit is the watt.
- When values of voltage and current are given, the power P = VI.
- When values for voltage and resistance are given then power P = V2 ÷ R.
- When values for current and resistance are given, then power = I2R.
Applications of Ohm’s Law
- Ohm’s law helps determine voltage, resistance, or current.
- It is used to maintain desired voltage drop across electronic components.
- Ohm’s law is used in the DC ammeter to divert current.
Limitations of Ohm’s Law
- Ohm’s is not applicable for unilateral electrical elements like diodes and transistors as they allow current to flow only in one direction.
- Non-linear electrical elements like capacitance and resistance, voltage, and current are not constant. Therefore, it is difficult to apply Ohm’s law
Electrical Resistance
R = ρl/A
l is the length of the conductor, A is the cross-section area, ρ is the resistivity of the material of a conductor
Factors that affect electrical resistance are the Cross-sectional area of the conductor, length of the conductor, the material of the conductor, and temperature of conducting material.
Resistivity
- Resistivity is a qualitative measurement of a material’s ability to resist flowing electric current.
- Insulators have a higher value of resistivity compared to conductors.
- The resistivity of a material of a conductor is given by ρ = m/n2 t.
- It depends on the nature and temperature of the material. Independent of other dimensions like length, area of cross-section, etc.
- It is low for metals, more for semiconductors, and high for alloys like nichrome, constantan, etc.
- In a magnetic field, the resistivity of metals increases but the resistivity of ferromagnetic materials decreases.
How Do Resistors Work?
Electric Resistivity
Electric resistivity is defined as the electrical resistance offered per unit length and unit cross-sectional area at a specific temperature. It is denoted by ρ. It is also known as specific electrical resistance. Its formula is:
ρ = E/J
E is the electric field, J is the current density
Electrical resistivity is the reciprocal of electrical conductivity and is a measure of the ability of a material to oppose the flow of current. Metals are good resistors of electricity and thus have low resistivity. Insulators such as rubber, glass, and graphite have high resistivity. Semiconductors resistivity decreases with an increase in temperature and is also affected by the presence of impurities.
Resistivity of Materials
Resistivity of Different Materials
The resistivity of different materials is listed in the table below:
- Formula of Resistivity: The materials with the electric field and current density have the given resistivity formula ie ρ = E/J. Here ρ is the resistivity of the material, E is the magnitude of the electric field and J is the magnitude of current density. Conductors with a uniform cross-section and uniform flow of electric current can use the formula ρ =R A/l.
- Resistor color coding: The resistance is indicated by using electronic color codes. It contains 4 bands. The first band indicates the first significant figure of resistance, the second band indicates the second significant figure, the third band indicates a decimal multiplier, and the fourth band indicates tolerance that the resistor can withstand. In the absence of the 4th band, a default tolerance of 20% is taken.
Resistor color coding
Important Notes on Resistors
- They reduce current flow and lower voltage levels within the circuit.
- It is a passive element ie it only consumes power but doesn’t generate.
- A circuit is composed of conductors like wire, power source, load, resistor, and switch.
- It starts and ends at the same point. In general, a copper wire without insulation is used as a conductor.
- In an electric circuit, different components are connected either in series or in parallel to produce different resistive networks.
- In the same circuit, resistors can be connected in both parallel and series across different loops to produce a more complex resistive network known as mixed resistor circuits.
Resistors in Series
- A circuit is connected in series when the same amount of current flows through the resistors.
- The voltage across each resistor is different.
- If any resistor is broken, then the entire circuit is turned off.
- The construction of a series circuit is simpler than a parallel circuit.
- The sum of potential differences across individual resistors is equal to the potential difference applied by the source.
- Equivalent resistance R = R1 + R2 + R3.
Resistors in Parallel
- A circuit is connected in parallel when the voltage is the same across the resistors.
- It can be connected or disconnected easily without affecting other elements in the circuit.
- The sum of electric currents flowing through individual resistors is equal to the electric current drawn from the source.
- Equivalent resistance 1/R = 1/(R1 + R2 + R3)
Cells, Electromotive Force and Internal Resistance
Electric Cell is a device that converts chemical energy into electrical energy. The battery provides the constant electromotive force to an electrical circuit. Each cell comprises 2 half cells connected in series by a conductive electrolyte containing anions and cations. One-half cell is made of electrolyte and negative electrode called an anion. The other half cell is made of electrolyte and positive electrode called cathode.
Redox reactions occur simultaneously. Cations are reduced at the cathode while charging while anions are oxidized at the anode while charging. Electrodes do not touch each other, they are electrically connected by the electrolyte.
Electromotive force (emf) of a cell
- The energy given by a cell in flowing unit positive charge throughout the circuit one time is equal to the emf of a cell.
- When there is no electrical equipment attached to the cell, then the electrolyte has the same potential (emf) throughout the cell.
- Condition of no current flowing through the cell is also known as an open circuit and it results in emf of a cell is equal to the difference in emf of electrodes.
- The potential difference between anode and cathode is known as EMF. It is represented as E =W/q.
- SI unit of electromotive force is volt.
Terminal Potential Difference of a cell
The energy given by a cell in flowing unit positive charge through till outer circuit one time from one terminal of cell to another terminal. It is represented as V = W/q. Its SI unit is volt.
Internal Resistance of a cell
- The obstruction offered by the electrolyte of a cell in the path of electric current.
- The internal resistance of a cell increases with an increase in the concentration of electrolytes.
- It also increases with an increase in distance between electrodes.
- It decreases with an increase in the area of electrodes dipped in the electrolyte.
- The relation between E, V, and r is E=V+Ir. Here r = (E/V-1)R.
- If the cell is in a charging state, then E =V-Ir.
Cells in Series and Parallel
- In Series: In n cells, each of emf E and internal resistance r are connected in series to resistance R, then equivalent emf is Eeq = E1 + E2 + …… +En = Ne. The Equivalent internal resistance req = r1 + r2 +…+rn = nr. The current in the circuit I = Eeq/(R+req) = nE/(R+nr).
- In Parallel: In n cells, each of emf E and internal resistance r is connected in parallel. The current in circuit I = E/(R+r/n).
- Mixed Grouping: In n cells, each of emf E and internal resistance r is connected in series, and such m rows are connected in parallel. The current in the circuit I=Ne/(R+nr/m) or I=mnE/mR + nr.
Kirchhoff’s Rules
There are two Kirchhoff’s laws to solve complicated electrical circuits. Using these laws and equations for individual components such as a resistor, capacitor, and inductor, we can analyze circuits.
- Junction Rule: The algebraic sum of all currents meeting at a junction in a closed circuit is zero. It follows the law of conservation of charge. In this rule, the total current entering the junction is the same as the charge leaving the junction as there is no charge lost. This current law can be applied to analyze parallel circuits.
- Loop Rule: The algebraic sum of all potential differences or voltage in any closed circuit is zero. It follows the law of conservation of energy. When you start at any point of the loop and continue in the same direction, voltage drops in all directions either negative or positive and returns to the same point. It should be noted that direction should either be maintained clockwise or counterclockwise or else the final voltage value will not be equal to zero. This voltage law is applied to analyze circuits in series.
Wheatstone Bridge
It is an arrangement of 4 resistances where one resistance is unknown while the rest are known. The bridge is said to be balanced when the deflection of the galvanometer is zero. The principle of the Wheatstone bridge is P/Q = R/S. The value of unknown resistance S can be found using the values of P, Q, and R.
Meter Bridge
It is the simplest form of Wheatstone Bridge and is used for comparing resistance accurately. The formula used to compare resistance is R/S = I1/(100 – I1). I1 is the length of the wire and it is from there, that a null point is obtained.
Potentiometer
It is an ideal device to measure the potential difference between the two points. It consists of long resistance wire AB of the uniform cross-section.
Potentiometer
If R is the total resistance of Potentiometer wire, L is total length, then the potential gradient will be K =V/L =IR/L = Eo R/(Ro + R)L where E0 is emf of battery and R0 is the resistance inserted using rheostat Rh.
Things to Remember
- The rate of flow of charge through any cross-section of a wire is known as electric current.
- The formulae of electric current (I) =q/t.
- The SI unit of Electric current is Ampere.
- The conventional direction of electric current is the direction of motion of the positive charge.
- As per the magnitude and direction of electric current it is of two types ie Direct Current and Alternating Current.
- The electric current flowing through the conductor is directly proportional to the potential difference (V) applied across its ends.
- Resistivity is a qualitative measurement of a material’s ability to resist flowing electric current.