Resistors circuits – problems and solutions

دوائر المقاومات - المشاكل والحلول

1. Which one of the resistors circuits, as shown in the figure below, has bigger resistance.

Resistors circuits – problems and solutions 1

Answer A

R₁ = 2 أوم، R₂= 2 أوم، R₃ = 6 أوم، R₄ = 6 أوم

R₃ و ر₄ يتم توصيلها على التوازي. المقاومة المكافئة:

1 / R₃₄ = 1/ر₃ + 1 / ص₄= 1/6 + 1/6 = 2/6

R₃₄= 6/2 = 3 أوم

R_1,R₂ و ر₃₄يتم توصيلها على التوالي. المقاومة المكافئة:

ص = ص₁ + R₂ + R₃₄= 2 Ω + 2 Ω + 3 Ω

R = 7 Ω

الإجابة ب

R₁ = 2 أوم، R₂= 4 أوم، R₃ = 4 أوم، R₄ = 8 أوم

R₂ و ر₃يتم توصيلها على التوالي. المقاومة المكافئة:

R₂₃ = ص₂ + R₃ = 4 أوم + 4 أوم = 8 أوم

R₂₃ و ر₄ يتم توصيلها على التوازي. المقاومة المكافئة:

1 / R₂₃₄ = 1/ر₂₃+ 1 / ص₄ = 1/8 + 1/8 = 2/8

R₂₃₄ = 8/2 = 4 أوم

R₁ و ر₂₃₄ يتم توصيلها على التوالي. المقاومة المكافئة:

ص = ص₁ + R₂₃₄ = 2 أوم + 4 أوم

R = 6 Ω

إجابة ج

R₁ = 9 أوم، R₂ = 9 أوم، R₃ = 9 أوم، R₄ = 2 أوم

R_1,R₂ و ر₃ يتم توصيلها على التوازي. المقاومة المكافئة:

1 / R₁₂₃= 1/ر₁+ 1 / ص₂ + 1 / ص₃= 1/9 + 1/9 + 1/9 = 3/9

R₁₂₃= 9/3 = 3 أوم

R₁₂₃و ر₄ يتم توصيلها على التوالي. المقاومة المكافئة:

ص = ص₁₂₃+ R₄= 3 أوم + 2 أوم

R = 5 Ω

Answer D

R₁ = 5 أوم، R₂= 10 أوم، R₃ = 2 أوم، R₄ = 2 أوم

R₁ و ر₂ يتم توصيلها على التوازي. المقاومة المكافئة:

1 / R₁₂ = 1/ر₁ + 1 / ص₂= 1/5 + 1/10 = 2/10 + 1/10

1 / R₁₂ = 3 / 10

R₁₂= 10/3 أوم

R₃ و ر₄ يتم توصيلها على التوازي. المقاومة المكافئة:

1 / R₃₄= 1/ر₃ + 1 / ص₄ = 1/2 + 1/2 = 2/2

R₃₄= 1 أوم

R₁₂و ر₃₄يتم توصيلها على التوالي. المقاومة المكافئة:

ص = ص₁₂+ R₃₄= 10/3 + 3/3 = 13/3

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R = 4.3 Ω

2. What is the equivalent resistor in the circuit as shown in figure below.

الحل: Resistors circuits – problems and solutions 2

Resistor 6 Ω, 3 Ω and 2 Ω are connected in parallel. The equivalent resistor :

1 / R_P = ١/٤ + ١/٤ + ١/٦ = ٣/١٢ + ٣/١٢ + ٢/١٢ = ٨/١٢

R_P = 6/6 = 1 أوم

Resistor 7 Ω, 8 Ω and 1 Ω are connected in series. The equivalent resistor :

R = 7 + 8 + 1 = 16 أوم

3. What is the equivalent resistor in the circuit as shown in figure below.

معروف :

المقاوم 1 (R₁) = 2 أوم Resistors circuits – problems and solutions 3

المقاوم 2 (R₂) = 2 أوم

المقاوم 3 (R₃) = 2 أوم

المقاوم 4 (R₄) = 2 أوم

مطلوب: The equivalent resistor

الحل:

المقاوم R₂ والمقاوم R₃ are connected in parallel. The equivalent resistor

1 / R₂₃ = 1/ر₂+ 1 / ص₃

1 / R₂₃ = 1/2 + 1/2 = 2/2

R₂₃ = 1 أوم

المقاوم R₁المقاوم R₂₃ والمقاوم R₃ يتم توصيلها على التوالي. المقاومة المكافئة:

ص = ص₁ + R₂+ R₃ = 2 + 1 + 2

R = 5 أوم

What is the primary function of a resistor in an electronic circuit?
- إجابة: A resistor’s primary function is to limit or control the flow of electric current in a circuit. It introduces resistance to the flow of electrons, which can be useful for controlling circuit behavior or protecting components.

How do series and parallel resistor configurations differ in terms of total resistance?
- إجابة: In a series configuration, the total resistance $R_{t o t a l}$ is the sum of individual resistances: $R_{t o t a l} = R_{1} + R_{2} + ...$ . In a parallel configuration, the inverse of the total resistance is the sum of the inverses of the individual resistances: 1/ $R ^{t o t a l} = 1 / R ^{1} + 1 / R ^{2} + ...$ .

Why might one choose to connect resistors in parallel rather than in series?
- إجابة: Connecting resistors in parallel can decrease the total resistance of a circuit, potentially increasing the total current flow. It can also provide redundancy—if one resistor fails, the circuit can still operate with the other parallel resistors.
How does the power rating of a resistor relate to its use in a circuit?
- إجابة: The power rating indicates the maximum amount of power the resistor can dissipate as heat without being damaged. If a resistor in a circuit dissipates power beyond its rating, it can overheat and fail.

Why do some circuits use variable resistors?
- إجابة: Variable resistors, like potentiometers or rheostats, allow for adjustable resistance in a circuit. This can be useful for tuning or adjusting circuit parameters, such as the volume in audio devices or the brightness of a light.
What happens if a resistor in a series circuit fails (opens)?
- إجابة: If a resistor in a series circuit fails by becoming an open circuit, the entire circuit will open, and no current will flow through it. It’s akin to having a break in a water pipeline.

What happens if a resistor in a parallel circuit fails (opens)?
- إجابة: If a resistor in a parallel circuit fails by becoming an open circuit, the rest of the parallel branches will still carry current. The total resistance of the circuit will increase since one of the parallel paths has been removed.
Why do some circuits utilize resistors with very high resistance values, sometimes in the order of megaohms?
- إجابة: High resistance values can be used for various purposes, such as creating voltage dividers, biasing transistors, or working with very low current applications. They can ensure minimal current flow in certain parts of circuits, especially where sensitivity or precision is needed.

How does temperature affect the resistance of most resistors?
- إجابة: For many materials, resistance increases with temperature. The amount by which resistance changes with temperature is defined by the material’s temperature coefficient of resistance. Some resistors are specifically designed to have minimal change in resistance with temperature (these are called temperature-stable or low temp-co resistors).
Why are pull-up and pull-down resistors used in digital circuits?

إجابة: Pull-up and pull-down resistors are used to define the default (idle) state of a digital input pin. A pull-up resistor connects an input pin to a positive voltage when no active signal is applied, ensuring a default HIGH state. Conversely, a pull-down resistor connects the input pin to ground, ensuring a default LOW state.