Electric Current (I)
Electric Current Density (J)
- For irregular shapes of cross-section
I, J and A are all scalar quantities.
Drift Velocity of Free Electrons in a Metallic Conductor
- E is the applies field, e is the charge of an electron, m is the mass of an electron and t is the time interval between successive collisions (relaxation time)
- The mobility μ of a charge carrier is defined as the drift velocity per unit electric field.
- R = Resistance of conductor
- Unit of Resistance; Volt/ampere, (Ω ohm)
Resistance and Resistivity
- The inverse of resistance is called conductance G.
- S.I. unit Ω-1 is called Siemens (S)
- The resistance of a conductor is directly proportional to its length l and inversely proportional to the area of cross-section A.
- The inverse of resistivity is called conductivity σ.
- S.I. unit is Ω-1n-1 or Sm-1
Temperature Coefficient of Resistance
- RT = Resistance at temperature T
- R0 = Resistance at temperature T0
- α = Temperature coefficient of resistance.
Temperature Coefficient of Resistivity (ρ)
- For conductors
- For insulators
- K = Boltzman constant
- T = Absolute temperature
Combination of Resistances
- Resistance In Series
- Resistance in Parallel
Internal Resistance of a Cell and Terminal Voltage
- First Rule (Junction Rule)
- Second Rule (Loop Rule)(Based on law of conservation of energy)
- The algebraic sum of changes in potential around any closed loop must be zero.
- The metre bridge
Shunt Resistance Required to Convert a Galvanometer into an Ammeter of Desired range
- Resistance of ammeter so obtained
Series Resistance Required to Convert a Galvanometer into a Voltmeter of Desired Range.
is desired range and R is additional series resistance.
Cell in Series and Parallel
Heating Effect of Current
- When a charge dq passes across a potential difference V, the work done dW is given by
dW = V dq
- The flow of charge dq in time dt is equivalent to current I.
- According to Ohm’s Law V = Ri
- Resistance of a bulb or other electrical appliances:
- And maximum current that can be passed without the appliance getting fused.
- Ratio of powers consumed in two resistors in series:
- Ratio of powers consumed in two resistors in parallel.
Faraday’s Laws of Electrolysis
- First Law
- The mass of a substance deposited or liberated at an electrode is proportional to the quantity of charge that passes through the electrolyte.
- Second Law
- If the same quantity of charge is passed through several electrolytes, then the masses of various substances deposited at the respective electrodes are proportional to their chemical equivalents.
- The constant F is called Faraday.
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