If two resistors R1 and R2 are connected in parallel, the equivalent resistance is always:

Question

Examoogle · Accepted Answer

The correct answer is Option B: Less than the smallest resistor. When resistors are connected in parallel, the total equivalent resistance is always less than the value of the smallest individual resistor in the network. This occurs because each additional parallel path provides an easier route for current to flow, effectively reducing the overall opposition.

Step-by-Step Solution & Concepts:
When resistors are connected in parallel, the total equivalent resistance is always less than the value of the smallest individual resistor in the network. This occurs because each additional parallel path provides an easier route for current to flow, effectively reducing the overall opposition.

Working Principle: In a parallel circuit, the voltage across each resistor is identical, while the total current is the sum of currents through each branch ($I_{total} = I_1 + I_2 + ... + I_n$). By applying Ohm's Law, the reciprocal of the equivalent resistance is the sum of the reciprocals of the individual resistances. Since adding more terms to the sum of reciprocals increases the value, the reciprocal of the total resistance becomes larger, which mathematically forces the equivalent resistance to decrease.

Key Formulas: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n}$ — Reciprocal formula for $n$ resistors in parallel; $R_{eq} = \frac{R_1 R_2}{R_1 + R_2}$ — Specific formula for two resistors in parallel

Key Points: The equivalent resistance is always lower than the minimum resistance in the combination.; Conductance adds linearly in parallel circuits ($G_{eq} = G_1 + G_2 + ... + G_n$).; If resistors are identical ($R$), then $R_{eq} = \frac{R}{n}$.

Advantages: Independent operation of branches; Total circuit resistance decreases with more branches

Disadvantages: Requires more wiring compared to series circuits; Voltage remains same but current demand increases

Applications: House wiring and distribution systems; Bypassing components in electronic circuits

Additional Info: Option A is incorrect because it describes series circuits ($R_{eq} = R_1 + R_2$).. Option C is incorrect as it describes series connection.. Option D is mathematically irrelevant for standard resistor combinations.

Answer: B is correct — The equivalent resistance of a parallel combination is always less than the smallest individual resistance.

Exam Tip: For quick calculation of two parallel resistors, use the formula $	ext{Product over Sum}$: $\frac{R_1 R_2}{R_1 + R_2}$.

Examoogle · Answer

Option A: Greater than the largest resistor

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Option C: Equal to the sum of resistors

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Option D: Equal to the difference of resistors

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