In the context of electronic components, if a number of resistances are connected and the reciprocal of the su

Question

In the context of electronic components, if a number of resistances are connected and the reciprocal of the sum of individual resistances is equal to the sum of reciprocals of individual resistances, then the type of connection is called _______.

Examoogle · Accepted Answer

The correct answer is Option A: parallel circuit. The condition described defines a parallel circuit where the reciprocal of the total equivalent resistance is equal to the sum of the reciprocals of individual resistances. Mathematically, for a parallel connection of $n$ resistors, the equivalent resistance $R_{eq}$ is determined by the relationship $\frac{1}{R_{eq}} = \sum_{i=1}^{n} \frac{1}{R_{i}}$.

Step-by-Step Solution & Concepts:
The condition described defines a parallel circuit where the reciprocal of the total equivalent resistance is equal to the sum of the reciprocals of individual resistances. Mathematically, for a parallel connection of $n$ resistors, the equivalent resistance $R_{eq}$ is determined by the relationship $\frac{1}{R_{eq}} = \sum_{i=1}^{n} \frac{1}{R_{i}}$.

Working Principle: In a parallel circuit, the voltage across each component remains the same, while the total current is the sum of currents through individual branches. Because the total current $I = I_{1} + I_{2} + ... + I_{n}$ and by Ohm's Law $I = \frac{V}{R}$, it follows that $\frac{V}{R_{eq}} = \frac{V}{R_{1}} + \frac{V}{R_{2}} + ... + \frac{V}{R_{n}}$. Dividing both sides by $V$ yields the reciprocal identity.

Key Formulas: $\frac{1}{R_{eq}} = \sum_{i=1}^{n} \frac{1}{R_{i}}$ — Equivalent resistance for $n$ resistors in parallel; $R_{eq} = R_{1} + R_{2} + ... + R_{n}$ — Equivalent resistance for $n$ resistors in series

Key Points: In parallel circuits, the equivalent resistance is always less than the smallest individual resistance in the network.; The reciprocal of resistance is known as conductance, denoted by $G$, measured in Siemens ($S$).; In a parallel connection, the total conductance is the sum of individual conductances: $G_{eq} = G_{1} + G_{2} + ... + G_{n}$.

Advantages: Individual components can be controlled or isolated without affecting others.; The voltage remains constant across all parallel branches.

Disadvantages: It cannot provide a voltage divider function like a series circuit.; Increased current draw as more components are added in parallel, which may lead to overloading.

Applications: Domestic wiring for lighting and appliances.; DC power distribution systems in electronics.

Additional Info: The condition provided in the question is the standard analytical definition for parallel resistive networks.. Option C (series circuit) is incorrect because for series circuits, the total resistance is the direct sum: $R_{eq} = R_{1} + R_{2} + ... + R_{n}$.

Answer: A is correct — The reciprocal relationship between total equivalent resistance and individual resistances is the defining characteristic of a parallel circuit connection.

Exam Tip: Remember that for parallel circuits, the equivalent resistance is always smaller than the smallest resistor, whereas for series circuits, it is always larger than the largest resistor.

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Option B: series–parallel circuit

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Option C: series circuit

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Option D: grouping circuit

Feature	Parallel Connection	Series Connection
Equivalent Resistance	$\frac{1}{R_{eq}} = \sum \frac{1}{R_{i}}$	$R_{eq} = \sum R_{i}$
Voltage Distribution	Same across all resistors	Distributed based on resistance

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