# 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.

- a source of voltage or potential difference (

- 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}*I*_{1}=*I*_{2}=*I*_{3}= … =*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}*V*_{1}+*V*_{2}+*V*_{3}+ … = ∑*V*_{i} - In a series circuit, the
*total resistance*equals the*sum*of the individual resistances.*R*=_{s}*R*_{1}+*R*_{2}+*R*_{3}+ … = ∑*R*_{i}- Resistance increases (and current decreases) as resistors are added in series to a source of constant voltage.

- In a series circuit,
- 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}*I*_{1}+*I*_{2}+*I*_{3}+ … = ∑*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}*V*_{1}=*V*_{2}=*V*_{3}= … =*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 *R*_{p}*R*_{1}*R*_{2}*R*_{3}*R*_{i} - Resistance decreases (and current increases) as resistors are added in parallel to a source of constant voltage.

- In a parallel circuit,
- 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.

- Current is measured with an ammeter.