Resistors in Circuits

Summary

• The basic components of a simple circuit are…
  • a source of voltage or potential difference (V) like a battery, power supply, solar cell, etc.
  • a device with a resistance (R) like a light, heater, motor, television, etc. identified by the generic name resistor.
  • wires of negligible resistance to carry current (I) on a closed loop from the voltage source to the resistor and back.

• Conservation of charge in a circuit
  • The current flowing into a component equals the current flowing out.
• Conservation of energy in a circuit
  • When current flows through a voltage source it experiences a voltage increase.
  • When current flows through a resistor it experiences a voltage drop.
  • When current flows around a circuit it experiences no change in voltage.
• The components in a series circuit are connected along a single path.
  • In a series circuit, current is the same everywhere.

    I_s = I₁ = I₂ = I₃ = … = I_i

  • In a series circuit, voltage divides so that the voltage increase supplied by the voltage source equals the sum of the voltage drops across the resistors.

    V_s = V₁ + V₂ + V₃ + … = ∑V_i

  • In a series circuit, the total resistance equals the sum of the individual resistances.

    R_s = R₁ + R₂ + R₃ + … = ∑R_i

    • Resistance increases (and current decreases) as resistors are added in series to a source of constant voltage.
• The components in a parallel circuit lie on independent branches.
  • In a parallel circuit, current divides so that the total current through the voltage source equals the sum of the currents through the branches.

    I_p = I₁ + I₂ + I₃ + … = ∑I_i

  • In a parallel circuit, the voltage increase across the voltage source is the same as the voltage drops across each branch.

    V_p = V₁ = V₂ = V₃ = … = V_i

  • In a parallel circuit, the inverse of the total resistance equals the sum of the inverses of the individual resistances.

    1	=	1	+	1	+	1	+ … = ∑	1
    Rp		R1		R2		R3		Ri

  • Resistance decreases (and current increases) as resistors are added in parallel to a source of constant voltage.
• Meters in circuits
  • Current is measured with an ammeter.
    • An ammeter is wired in series with the circuit element or section of the circuit being examined.
    • An ideal ammeter has zero resistance so that it does not increase the resistance and reduce the current.
    • The symbol for an ammeter is an uppercase A⃝ in a circle.
  • Voltage is measured with a voltmeter.
    • A voltmeter is wired parallel to the circuit element or section of the circuit being examined.
    • An ideal voltmeter has infinite resistance so that it does not decrease the resistance and increase the current (so that is does not short the circuit).
    • The symbol for a voltmeter is an uppercase V⃝ in a circle.
  • Resistance is measured with an ohmmeter.
    • An ohmmeter combines a power supply with an ammeter and a voltmeter.
    • An ohmmeter "computes" resistance from the ratio of voltage to current.
    • The symbol for an ohmmeter is an uppercase Greek Ω⃝ (omega) in a circle.