current-voltage characteristic

Examples of current-voltage characteristic in the following topics:

• Different Types of Currents

  • A resistive circuit is a circuit containing only resistors and ideal current and voltage sources.
  • In this case, the circuit voltages and currents are independent of time.
  • A particular circuit voltage or current does not depend on the past value of any circuit voltage or current.
  • This solution gives the circuit voltages and currents when the circuit is in DC steady state.
  • The two Kirchoff laws along with the current-voltage characteristic (I-V curve) of each electrical element completely describe a circuit.

• RL Circuits

  • An RL circuit consists of an inductor and a resistor, in series or parallel with each other, with current driven by a voltage source.
  • When the switch is first moved to position 1 (at t=0), the current is zero and it eventually rises to I0=V/R, where R is the total resistance of the circuitand V is the battery's voltage.
  • The initial current is zero and approaches I0=V/R with a characteristic time constant for an RL circuit, given by:
  • The characteristic time $\tau$ depends on only two factors, the inductance L and the resistance R.
  • Describe current-voltage relationship in the RL circuit and calculate energy that can be stored in an inductor

• Voltmeters and Ammeters

  • Voltmeters and ammeters are used to measure voltage and current, respectively.
  • Voltmeters and ammeters measure the voltage and current, respectively, of a circuit.
  • The two crucial characteristics of any galvanometer are its resistance and its current sensitivity.
  • Current sensitivity is the current that gives a full-scale deflection of the galvanometer's needle -- in other words, the maximum current that the instrument can measure.
  • By connecting resistors to this galvanometer in different ways, you can use it as either a voltmeter or ammeter to measure a broad range of voltages or currents.

• Inductors in AC Circuits: Inductive Reactive and Phasor Diagrams

  • The graph shows voltage and current as functions of time.
  • The current then becomes negative, again following the voltage.
  • Current lags behind voltage, since inductors oppose change in current.
  • The voltage across an inductor "leads" the current because of the Lenz's law.
  • (b) Graph of current and voltage across the inductor as functions of time.

• EMF and Terminal Voltage

  • All voltage sources create a potential difference and can supply current if connected to a resistance.
  • However, emf differs from the voltage output of the device when current flows.
  • However, if the device's output voltage can be measured without drawing current, then output voltage will equal emf (even for a very depleted battery).
  • The larger the current, the smaller the terminal voltage.
  • Since V=emf−Ir, terminal voltage equals emf only if there is no current flowing.

• Current and Voltage Measurements in Circuits

  • The electrical current is directly proportional to the voltage applied and inversely related to the resistance in a circuit.
  • According to Ohm's law, The electrical current I, or movement of charge, that flows through most substances is directly proportional to the voltage V applied to it.
  • Using this equation, we can calculate the current, voltage, or resistance in a given circuit.
  • If we know the current and the resistance, we can rearrange the Ohm's law equation and solve for voltage V:
  • Describe the relationship between the electrical current, voltage, and resistance in a circuit

• Ohm's Law

  • Ohm's Law states that current is proportional to voltage; circuits are ohmic if they obey the relation V=IR.
  • Recall that while voltage drives current, resistance impedes it.
  • Ohmic materials have a resistance R that is independent of voltage V and current I.
  • If voltage is forced to some value V, then that voltage V divided by measured current I will equal R.
  • Or if the current is forced to some value I, then the measured voltage V divided by that current I is also R.

• The Hall Effect

  • When current runs through a wire exposed to a magnetic field a potential is produced across the conductor that is transverse to the current.
  • The Hall effect is the phenomenon in which a voltage difference (called the Hall voltage) is produced across an electrical conductor, transverse to the conductor's electric current when a magnetic field perpendicular to the conductor's current is applied.
  • For a metal containing only one type of charge carrier (electrons), the Hall voltage (VH) can be calculated as a factor of current (I), magnetic field (B), thickness of the conductor plate (t), and charge carrier density (n) of the carrier electrons:
  • The Hall coefficient (RH) is a characteristic of a conductor's material, and is defined as the ratio of induced electric field (Ey) to the product of current density (jx) and applied magnetic field (B):
  • Express Hall voltage for a a metal containing only one type of charge carriers

• Resistors and Capacitors in Series

  • When there is no current, there is no IR drop, so the voltage on the capacitor must then equal the emf of the voltage source.
  • Initially, voltage on the capacitor is zero and rises rapidly at first since the initial current is a maximum.
  • The voltage approaches emf asymptotically since the closer it gets to emf the less current flows.
  • Initially, the current is I0=V0/R, driven by the initial voltage V0 on the capacitor.
  • As the voltage decreases, the current and hence the rate of discharge decreases, implying another exponential formula for V.

• Phase Angle and Power Factor

  • In a series RC circuit connected to an AC voltage source, voltage and current maintain a phase difference.
  • As we studied in a previously Atom ("Impedance"), current, voltage and impedance in an RC circuit are related by an AC version of Ohm's law: $I = \frac{V}{Z}$, where I and V are peak current and peak voltage respectively, and Z is the impedance of the circuit.
  • we notice that voltage $v(t)$ and current $i(t)$ has a phase difference of $\phi$.
  • Because voltage and current are out of phase, power dissipated by the circuit is not equal to: (peak voltage) times (peak current).
  • The fact that source voltage and current are out of phase affects the power delivered to the circuit.