Current Electricity
Class 12 Physics · Physics Part I · Chapter 3
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Summary
Electric current is the rate of flow of charge, \(I=\dfrac{dq}{dt}\), arising from the drift of free electrons under an applied field. The average drift speed \(v_d=\dfrac{eE\tau}{m}\) leads to \(I=neAv_d\). Ohm's law states that for many conductors current is proportional to potential difference, \(V=IR\), where resistance \(R=\rho\dfrac{l}{A}\) depends on geometry and the material's resistivity \(\rho\). Resistivity rises with temperature for metals and falls for semiconductors. Resistors combine in series as \(R_s=R_1+R_2+\cdots\) and in parallel as \(\tfrac{1}{R_p}=\tfrac{1}{R_1}+\cdots\). A real cell has an emf \(\varepsilon\) and an internal resistance \(r\), so its terminal voltage is \(V=\varepsilon-Ir\). Kirchhoff's junction rule (charge conservation) and loop rule (energy conservation) solve complex networks. The Wheatstone bridge is balanced when \(\dfrac{R_1}{R_2}=\dfrac{R_3}{R_4}\), a principle exploited by the meter bridge and potentiometer for precise measurement. Electrical power dissipated is \(P=VI=I^2R=\dfrac{V^2}{R}\), and the heat produced obeys Joule's law.
Current and drift velocityOhm's law and resistivitySeries and parallel resistorsEmf and internal resistanceKirchhoff's rules and Wheatstone bridgeElectrical power and Joule heating
Key terms
Electric current
Rate of flow of charge, \(I=dq/dt\); SI unit ampere.
Drift velocity
Average velocity gained by free electrons under a field, \(v_d=eE\tau/m\).
Resistivity
Intrinsic material property \(\rho\) with \(R=\rho l/A\); unit \(\Omega\,m\).
Emf
Energy supplied per unit charge by a source, equal to terminal voltage on open circuit.
Internal resistance
Opposition to current within a cell, giving \(V=\varepsilon-Ir\).
Kirchhoff's rules
Junction rule (charge conservation) and loop rule (energy conservation) for circuits.
Extra questions & answers
Try one from this chapter
Drift velocity of electrons in a conductor is given by: