Resistance
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- Solving Resistance for Resistors in Series
Find the total resistance of the circuit. - Solving Resistance for Resistors in Parallel
Find the total resistance of the circuit. - Solving for Resistors in BOTH Series & Parallel Configurations
- Solving for More Resistors in BOTH Series & Parallel Configurations
Find the total resistance for the entire circuit.
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Topic Notes
In this lesson, we will learn:
- A review on what is an electric circuit and the main components: battery (voltage), closed wire path (current), and devices/resistors that use up electricity (resistance).
- What is resistance?
- What is the difference between connecting your circuit in series vs. parallel configurations for resistors?
- What is a battery and how does it provide voltage for an electric circuit?
- How to solve resistance problems for both series and parallel circuits by using the summation equations for equivalent resistance in series and equivalent resistance in parallel
- Req(series)=R1+R2+R3+...+Rn=∑k=1nRk
- Req(parallel)1=R11+R21+R31+...+Rn1=Rn=∑k=1nRk
- OR: Req(parallel)=R11+R21+R31+...Rn11=∑k=1nRk11
Notes:
- Resistance is a property of the electronic device (resistor; or even battery and wires can have some resistance too and use up some voltage)
- It is a measure of how difficult it is for charges to travel through the circuit
- Resistors in a circuit represent electronic devices that use up voltage
- The greater the resistance, the bigger the voltage drop
- Resistances of metals are CONSTANT and INDEPENDENT of voltage
- The unit for resistance is the ohm (Ω) and can be determined for a circuit by dividing the voltage by the current (in preview of Ohm’s law: V=IR).
- When solving for resistance in series, we must use the summation equation:
- Req(series)=R1+R2+R3+...+Rn=∑k=1nRk
- Where all resistors in series are added up for the total resistance
- Thus, Req(series) is greater than any single RK independently; adding more resistors in series will increase the total resistance
- When solving for resistance in parallel, we must use the summation equation:
- Req(parallel)1=R11+R21+R31+...+Rn1=Rn=∑k=1nRk
- OR: Req(parallel)=R11+R21+R31+...Rn11=∑k=1nRk11
- Where the total resistance is equal to the inverse of the sum of all inverses of resistors (branches) in parallel
- Thus, Req(parallel) is less than any single RK independently; adding more resistors in parallel will decrease the total resistance
- In terms of resistance, the advantage of a series configuration is that the battery will last longer; the greater the resistance, the more difficult it is for the charges to travel; thus, less charge is drawn out of the battery over time (less current)
- A parallel configuration generates lesser resistance, allowing charges to flow freely; thus, more charge is drawn out of the battery over time (more current)
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