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ADV 1: DC Circuits and Resistors

ADV 1: DC Circuits and Resistors. Introductory mini-lecture. Potential difference = Voltage. Batteries inject electric potential energy U into a circuit and a load (e.g. a resistor) dissipates that energy.

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ADV 1: DC Circuits and Resistors

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  1. ADV 1: DC Circuits and Resistors Introductory mini-lecture

  2. Potential difference = Voltage • Batteries inject electric potential energy U into a circuit and a load (e.g. a resistor) dissipates that energy. • The potential difference across a battery is U per unit charge – measured in volts – i.e. V =U/q • We lazily talk about voltage V (often at a point) in a circuit when we really mean potential difference, which would be better represented as Vb - Vaor Vab.

  3. Voltage and Kirchhoff’s Loop Law • The electric field is conservative, so Vab is independent of the path from a to b … but don’t forget the signs of the potential differences. • Kirchhoff’s Loop Law: the algebraic sum of voltages around any closed loop is zero _

  4. Current and Kirchhoff’s Junction Law • Current I measures the flow of charge dQ per time interval dt, I = dQ/dt Units are amperes (A): 1A = 1 C/s = 6.2 x1018 electrons/s • Kirchhoff’s junction law: algebraic sum of currents flowing into any junction = the algebraic sum of currents flowing out of the junction

  5. Resistance and Ohm’s Law • Resistance R quantifies how easily current can flow • For a fixed current I, larger R means more energyis required to make the current flow • R(I) = V/I defines the resistance at a given current I • Ohmic materials: resistance independent of current Ohm’s Law: V=IR

  6. Resistance and Ohm’s Law

  7. Resistances in series • Currents through two resistors in series are equal by Kirchhoff’s junction law • Voltage drop across two resistors in series: Vtotal = I(R1+R2)

  8. Voltage dividers • A voltage divider is a simple circuit that produces an output voltage Vout that is a proportion of the input voltage Vin • Vout/Vin is set by the relative values of R1 and R2 , i.e., the input voltage is divided between R1 and R2 .

  9. Voltage dividers

  10. Resistances in parallel • Current divides in inverse proportion to the resistance, i.e., the smaller resistance carries the greater current. • Voltage drops across two resistors in parallel are equal by Kirchhoff’s loop law

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