Electrical Laws and Theorems:
Ohm’s law states that the current I flowing in a circuit is directly proportional to the applied voltage V and inversely proportional to the resistance R, provided the temperature remains constant.
Laws of Electromagnetic Induction
Faraday’s laws of Electromagnetic Induction:
(i) An induced e.m.f. is set up whenever the magnetic field linking that circuit changes.
(ii) The magnitude of the induced e.m.f. in any circuit is proportional to the rate of change of the magnetic flux linking the circuit.
Lenz’s law:(Direction of Induced EMF)
The direction of an induced e.m.f. is always such that it tends to set up a current opposing the motion or the change of flux responsible for inducing that e.m.f.
An alternative method to Lenz’s law of determining relative directions is given by Fleming’s Right-hand rule (the Generator rule).
Fleming’s Right-hand rule:
Let the thumb, first finger and second finger of the right hand be extended such that they are all at right angles to each other. If the first finger points in the direction of the magnetic field, the thumb points in the direction of motion of the conductor relative to the magnetic field, then the second finger will point in the direction of the induced e.m.f.
The direction of the force exerted on a conductor can be pre-determined by using Fleming’s left-hand rule (often called the motor rule).
Fleming’s left-hand rule:
Let the thumb, first finger and second finger of the left hand be extended such that they are all at right-angles to each other. If the first finger points in the direction of the magnetic field, the second finger points in the direction of the current, then the thumb will point in the direction of the motion of the conductor.
DC Circuit Theory Theorems:
(a) Current Law:
At any junction in an electric circuit the total current flowing towards that junction is equal to the total current flowing away from the junction.
(b) Voltage Law:
In any closed loop in a network, the algebraic sum of the voltage drops (i.e. products of current and resistance) taken around the loop is equal to the resultant e.m.f. acting in that loop.
In any network made up of linear resistances and containing more than one source of e.m.f., the resultant current flowing in any branch is the algebraic sum of the currents that would flow in that branch if each source was considered separately, all other sources being replaced at that time by their respective internal resistances.
The current in any branch of a network is that which would result if an e.m.f. equal to the p.d. across a break made in the branch, were introduced into the branch, all other e.m.f.’s being removed and represented by the internal resistances of the sources.
The current that flows in any branch of a network is the same as that which would flow in the branch if it were connected across a source of electrical energy, the short-circuit current of which is equal to the current that would flow in a short-circuit across the branch, and the internal resistance of which is equal to the resistance which appears across the open-circuited branch terminals.
Maximum Power Transfer Theorem:
The power transferred from a supply source to a load is at its maximum when the resistance of the load is equal to the internal resistance of the source.
The direction of the magnetic lines of flux is given by the screw rule.
If a normal right-hand thread screw is screwed along the conductor in the direction of the current, the direction of rotation of the screw is in the direction of the magnetic field.