Voltage, also known as electric potential difference, is a measure of the electrical energy per unit charge in an electrical circuit. It is expressed as the difference in electric potential between two points in a circuit, and is usually measured in units of volts (V).
The mathematical expression for voltage is given by the formula V = IR, where V represents the voltage, I represents the current flowing through the circuit, and R represents the resistance of the circuit. This formula is commonly known as Ohm’s law, which states that the voltage across a circuit is directly proportional to the current flowing through it, and is inversely proportional to the resistance of the circuit.
To put it simply, if the current flowing through a circuit increases, the voltage across the circuit will also increase, assuming the resistance remains constant. On the other hand, if the resistance of the circuit increases, the voltage across the circuit will decrease, assuming the current remains constant.
It should also be noted that voltage can vary over time, depending on changes in current or resistance. In such cases, the mathematical formula for voltage is given by V(t) = V0 + A sin(ωt + φ), where V0 represents the steady-state voltage or DC offset, A represents the amplitude of the alternating current (AC) voltage, ω represents the angular frequency of the AC voltage, t represents the time, and φ represents the phase angle of the AC voltage.
This formula describes a sinusoidal voltage waveform, which is commonly observed in AC circuits. The voltage waveform oscillates between positive and negative values, with the amplitude and frequency of the waveform determining the amount and rate of energy transfer in the circuit.
In conclusion, the mathematical formula for voltage is V = IR, which relates the voltage across a circuit to the current flowing through it and the resistance of the circuit. Additionally, voltage can also be expressed as a function of time, using a sinusoidal waveform formula that describes the amplitude, frequency, and phase angle of the voltage in an AC circuit.