The Physics
Hypertextbook
Opus in profectus

# 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.

Is = I1 = I2 = I3 = … = Ii

• 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.

Vs = V1 + V2 + V3 + … = ∑ Vi

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

Rs = R1 + R2 + R3 + … = ∑ Ri

• 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.

Ip = I1 + I2 + I3 + … = ∑ Ii

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

Vp = V1 = V2 = V3 = … = Vi

• 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.