Solving complex circuits

So, now we will solve the complex circuit with more than one series and parallel combinations.

1. As seen, the resistors 10 and 5 ohm are connected end to end and also the ending point of 10-ohm resistor is joined to starting point of 5-ohm resistor so we add them because for total resistance in series, we need to add all resistors.

2. Now three resistors 10Ω, 15Ω, and 20Ω are in parallel best the starting part is connected to starting part of other resistors so we will solve it according to parallel circuits.

Equivalent Resistance = 1/ ((1/10Ω) + (1/15Ω) + (1/20Ω))
= 4.615Ω

Now after simplifying the circuit have become very simple we just need to add the resistors in series

Total Resistance of circuit = 5Ω + 4.61Ω
= 9.61Ω

Applications

1. Voltage Division: Combining resistors in series forms a voltage divider circuit, useful for generating fractionally scaled output voltages.
2. Current Limiting: Series resistors restrict current to prevent component damage, ensuring safe operation.
3. LED Current Control: Series resistors prevent LEDs from exceeding safe current levels, extending their lifespan.
4. Pull-Up/Pull-Down Resistors: Series-connected resistors set default logic levels in digital circuits, preventing unstable inputs.
5. Signal Filtering: Series resistors, paired with capacitors, create filters for shaping signal frequencies.
6. Thermistor Networks: Series-connected thermistors and fixed resistors yield temperature-dependent voltage outputs, valuable for temperature sensing.
7. Wheatstone Bridge: Four resistors in a diamond pattern form a Wheatstone bridge for measuring unknown resistances.
8. Precision Resistor Networks: Series-connected resistors create accurate resistance values, important in precise analog designs.
9. Load Distribution: Series resistors aid in distributing current among devices sharing a power supply, ensuring even power delivery.

Advantages of Series Resistance:

1. Collective Resistance: Series resistance enables us to attain our desired resistance in the circuit just by adding up all the resistances.
2. Consistent Current: Same amount of current flows through all the components in the circuit which simplifies the working and calculation of the circuit.
3. Voltage Distribution: Series setups naturally distribute total voltage based on component resistances, making it useful for applications requiring specific voltage divisions.
4. Sequential Management: Components in series are linked end-to-end, facilitating sequential control or activation, as seen in LED light strings.

Disadvantages of Series Resistance:

1. Increased Total Resistance: Each resistor added in series raises the total resistance, potentially hindering efforts to minimize resistance or increase current.
2. Voltage Drop Across Each Resistor: Voltage drop accumulates across each resistor in series, leading to notable voltage loss across the circuit, unsuitable for steady voltage needs.
3. Single Failure Point: Failure or disconnection of one resistor disrupts the entire circuit, impacting current flow through the entire series.
4. Restricted Flexibility: Modifying resistance in series necessitates adding or changing resistors, providing less flexibility compared to parallel circuits.
5. Complexity with Varied Components: Integrating resistors with diverse tolerances or temperature coefficients in a series circuit can yield less predictable and manageable overall behavior.

Resistors are devices that obstruct the flow of electric current in the circuit. They provide the hindrance to the path of the current which flows in the circuit.

A resistor is a two-terminal electrical component that works by reducing the flow of charge and voltage levels in the circuit. Most of the circuits have one or more resistors to oppose the flow of current and balance the circuit. Most commonly there are two combinations of resistors – Resistors in Series and Parallel.