Electric Current And Circuit

We can use Ohm's Law to calculate the internal resistance of the cell. The total voltage in the circuit is given by the e.m.f. of the cell, and the total resistance in the circuit is the sum of the internal resistance and the external resistance . The formula we use is: where:
- e.m.f. = 0.5 V,
- = 0.75 A,
- = 1.9 ,
- is the internal resistance of the cell.
Substitute the values into the formula: Now, solve for : Now, calculate : Thus, the internal resistance of the cell is approximately 0.2 ohms.

The given circuit consists of resistors of values , , and , with a voltage difference between points and . We need to find the equivalent resistance when: - (i) , - (ii) .
For this circuit, when , the resistors will be connected in series, and the equivalent resistance is the sum of the individual resistances. Thus, the equivalent resistance will be:
For the second case, when , the resistors will be in parallel. The equivalent resistance for parallel resistors is given by the reciprocal sum of the individual resistances:
Solving this:
Thus, the equivalent resistance is:

Mutual Induction is the phenomenon in which a change in current in one coil induces a voltage in another coil that is placed nearby. The amount of voltage induced in the secondary coil depends on the rate of change of current in the primary coil. Mutual induction occurs when two coils are magnetically coupled, and the changing magnetic field from the primary coil induces an electromotive force (e.m.f.) in the secondary coil.
The mutual inductance between two coils is defined as the ratio of the induced e.m.f. in one coil to the rate of change of current in the other coil. The formula for mutual inductance is:
Where:
- is the mutual inductance in henries (H),
- Induced e.m.f. is the voltage induced in the secondary coil,
- is the rate of change of current in the primary coil.
Given:
- Induced e.m.f. = 40 kV = ,
- Initial current ,
- Final current = 0 (current reduces to zero),
- Time interval .
First, calculate the rate of change of current:
Now, substitute the values into the formula for mutual inductance:
Thus, the mutual inductance between the primary and secondary coils is .

Working Principle of a Transformer:
A transformer works on the principle of mutual induction. It consists of two coils: the primary coil and the secondary coil, wound on a common iron core. When an alternating current is passed through the primary coil, it creates a changing magnetic field, which induces a voltage in the secondary coil. The voltage ratio between the primary and secondary coils is proportional to the ratio of the number of turns in each coil. For an ideal transformer, the input power is equal to the output power. The voltage and current are related by the following equations:
Where:
- and are the voltages in the primary and secondary coils,
- and are the number of turns in the primary and secondary coils,
- and are the currents in the primary and secondary coils.
Given: - Number of turns ratio ,
- Input voltage ,
- Output current .
Step 1: Calculate the current in the primary coil.
Using the current ratio equation:
Thus, the current in the primary coil is:
So, the current in the primary coil is .
Step 2: Calculate the output power.
The output power is given by:
From the voltage ratio, we can find the secondary voltage:
Thus, the output power is:
Thus, the output power is .

Wattless current refers to the current that flows in an AC circuit when the voltage and current are out of phase with each other by 90 degrees. This happens in circuits that contain purely inductive or purely capacitive elements. In such cases, the power consumed by the circuit is zero because the current and voltage are not in phase, meaning that the energy supplied to the circuit is stored and returned (in the case of inductance or capacitance) without being dissipated as heat.
For example, in a purely inductive circuit, the current lags the voltage by 90° and the power factor is zero, meaning no real power is consumed. This results in wattless current, as the average power over a complete cycle is zero.

Core definition.
The electromotive force (emf) of a cell is the work done by the cell’s non-electrostatic (chemical) forces in moving unit positive charge once around the entire circuit (including the cell’s interior).
Mathematically, where is the work performed by the cell on charge . Its SI unit is the volt (V) .
Physical interpretation.
Inside the cell, chemical reactions separate charges against the internal electric field. This “source” work per unit charge is the emf. When no current flows (open circuit), the terminal potential difference equals .
Circuit relation (with internal resistance).
If the cell has internal resistance and supplies a current to an external circuit of resistance , then the terminal voltage is Thus represents the “total available push” per unit charge; a portion is lost inside the cell.
Integral form (general).
More generally, for any source, the line integral of the non-electrostatic force per unit charge around the loop (chemical, mechanical, photovoltaic, etc.).
Key properties.
is independent of load in the ideal (no internal resistance) case; real cells show a drop in terminal voltage under load due to .
Dimensions: (volt).