Comprehensive Study Guide on Electrical Current, Resistance, and Power

Definition of Electrical Current: Electrical current is defined specifically as the charge per unit time. It represents the rate at which electric charge flows through a cross-section of a conductor. Mathematically, it can be expressed as: $I = \frac{\Delta Q}{\Delta t}$ where $I$ is the current, $Q$ is the electrical charge, and $t$ is time.
- It is important to distinguish current from other concepts: it is not the same as electrical charge itself, nor is it the product of charge and time, nor the product of charge and potential difference.
Standard Unit of Current: The standard unit for measuring electric current is the $ampere$ . Other units mentioned in the context of electrical circuits include the $ohm$ (unit of resistance), the $watt$ (unit of power), and the $volt$ (unit of potential difference).

Series Connections: When resistances are connected in series, they are arranged in a single path. Consequently, all resistances connected in series have the same current flowing through them. They do not necessarily have the same potential difference or the same charge.
Parallel Connections: When resistances are connected in parallel, they are connected across the same two nodes. As a result, all resistances connected in parallel have the same potential difference (also referred to as voltage) across them. In this configuration, the current may vary across different branches depending on the individual resistance values.

Power Supplied by a Battery: The power provided by a battery to a circuit is calculated as the potential difference times the current. The formula is: $P = V \times I$ where $P$ is power, $V$ is the potential difference, and $I$ is the current. It is not calculated by dividing potential difference by current or by multiplying potential difference by the square of the current.
Power Dissipated by a Resistance: The power that is dissipated (usually as heat) by a resistor can be calculated using the relationship between current and resistance. It is defined as the square of the current times the resistance. The formula is: $P = I^2 \times R$ where $P$ is the dissipated power, $I$ is the current flowing through any given resistance, and $R$ is the resistance value.
Standard Unit of Power: The standard unit for electrical power is the $watt$ . One $watt$ is equivalent to one joule per second. This is distinct from the $volt$ (potential difference), the $ampere$ (current), and the $coulomb$ (electrical charge).

Voltmeter Connection Requirements: A voltmeter is a device used to measure the potential difference between two points in a circuit. To ensure an accurate measurement without significantly altering the circuit's flow, a voltmeter is always connected in parallel with the specific element whose potential difference is being measured.