Resistors - Maple Help

Resistors

Background

 Resistance What is resistance in a circuit?   By definition, an electrical circuit is a closed path where electrons flow. Resistance is the hindrance of the flow of electrons in a circuit. Electrons do not flow through the circuit in a direct path. Rather, electrons traverse the circuit in a zigzag fashion dictated by the collisions with the atoms of the medium of travel. These collisions hinder the movement of electrons and hence add resistance to the circuit.   What are the factors that affect resistance?   Length of path - The longer the path, the more places where collisions can occur and the more resistance occurs in the circuit. Cross sectional area of path - A wider path means that more current can flow through the path at the same time. Because electrons flow at higher rates through paths with greater cross sectional areas, less resistance occurs in the circuit. Material of path - Various materials have different conductive abilities. Consequently, bad conductors will increase resistance in a circuit, compared to good conductors.   What is a resistor?   A resistor is a passive electronic component (it does not have its own source of power) that reduces the electron flow through a circuit, thereby adding resistance to the circuit. It does this by using the aforementioned factors and is also engineered to maintain a specific resistance value over a range of conditions. Energy that the resistors remove from the circuit is lost in the form of heat. An ideal resistor behaves as dictated by Ohm's law: $I=\frac{\mathrm{ΔV}}{R}$ , where $\mathrm{ΔV}$ is the potential difference or voltage across the resistor in volts (V), $R$ is the resistance value of the resistor in ohms (Ω) and $I$ is the current that flows through the resistor in amps (A).   Resistors can be combined in series and parallel to make more complicated circuits. On a physical resistor component, the colors of the bands on the resistor describe the resistance value (Ω) of the resistor. Typically, there are four bands and the color values are read from left to right. The last or fourth band is usually gold or silver. The first two bands represent the value of the resistor and the third band represents the multiplier. The fourth band represents the tolerance value of the resistor and is a percentage indicating the range over that the actual resistance value may deviate from the intended one. For example, a 5% tolerance means the resistor is within ±5% of the intended value.

In the activity below, use the left hand set of Combo Boxes to find out the resistance of a resistor based on its color code, or use the right hand set of Combo Boxes to find out what the specific resistance of a resistor looks like.

 First Band: BlackBrownRedOrangeYellowGreenBlueVioletGrayWhite   Second Band: BlackBrownRedOrangeYellowGreenBlueVioletGrayWhite   Third Band: SilverGoldBlackBrownRedOrangeYellowGreenBlueViolet   Fourth Band: SilverGoldBrownRedGreenBlueVioletGray First Digit: 0123456789   Second Digit: 0123456789   Multiplier: 1101001000100001000001000000100000000.10.01   Tolerance: 105210.50.250.10.05%

To verify, you can use the resistance values from the resistor color code chart below.

 Color 1st Digit (Band 1) 2nd Digit (Band 2) Multiplier (Band 3) Tolerance % (Band 4) Black 0 0 1 - Brown 1 1 10 ±1 Red 2 2 100 ±2 Orange 3 3 1k - Yellow 4 4 10k - Green 5 5 100k ±0.5 Blue 6 6 1M ±0.25 Violet 7 7 10M ±0.1 Gray 8 8 - ±0.05 White 9 9 - - Gold - - 0.1 ±5 Silver - - 0.01 ±10

 More MathApps