In electrical circuits, understanding the relationship between resistance, energy, and power is crucial. Resistance acts as an internal friction that charges encounter as they move through a conductor, leading to energy loss. This energy loss can be quantified using the equation for the change in energy, represented as Δu = q × Δv, where q is the charge and Δv is the potential difference.
Power, defined as the rate at which energy changes, is expressed mathematically as P = Δu / Δt, where Δt is the time interval. This relationship allows us to derive the equation P = V × I, applicable to all circuit elements, including batteries and resistors. Here, V is voltage and I is current.
To derive this equation, we substitute Δu with q × Δv in the power equation. Notably, q / Δt defines current (I), leading to the simplified form P = V × I.
For resistors, Ohm's law, expressed as V = I × R, allows us to derive two additional forms of the power equation: P = I² × R and P = V² / R. Each of these equations is valid and can be used depending on the known variables in a problem.
The energy dissipated by resistors primarily manifests as heat due to internal friction. This heat generation is evident in everyday appliances like light bulbs, toasters, and hairdryers, which convert electrical energy into thermal energy.
For example, if a battery outputs 540 watts at a voltage of 9 volts, the current can be calculated using P = V × I. Rearranging gives I = P / V, resulting in a current of 60 amps.
In another scenario, if a resistor with a resistance of 30 kilo-ohms is connected to a circuit with a current of 60 milliamps, the power dissipated can be calculated using P = I² × R. This results in a power dissipation of 108 watts. To find the energy released in one minute, we use the relationship Δu = P × Δt, yielding an energy release of 6,480 joules.
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