The total resistance of two resistors R1 and R2 connected in series is:

Question

Examoogle · Accepted Answer

The correct answer is Option C: $R_1 + R_2$. When resistors are connected in series, the same current flows through each resistor, and the total resistance of the circuit is simply the arithmetic sum of the individual resistances. This ensures that the effective resistance is always greater than any single individual resistor in the series combination.

Step-by-Step Solution & Concepts:
When resistors are connected in series, the same current flows through each resistor, and the total resistance of the circuit is simply the arithmetic sum of the individual resistances. This ensures that the effective resistance is always greater than any single individual resistor in the series combination.

Working Principle: According to Ohm's Law ($V = IR$), the total potential difference across a series circuit is the sum of the potential drops across each resistor: $V = V_1 + V_2 + ... + V_n$. Since current ($I$) is constant in series, we substitute $V_1 = I R_1$ and $V_2 = I R_2$ into the equation $I R_{	ext{eq}} = I R_1 + I R_2$, which simplifies to $R_{	ext{eq}} = R_1 + R_2$.

Key Formulas: $R_{	ext{eq}} = R_1 + R_2 + ... + R_n$ — Total resistance in series connection; $V = IR$ — Ohm's Law relating voltage, current, and resistance

Key Points: The current through each resistor in a series circuit is identical.; The total resistance of a series combination is always higher than the largest individual resistor.; If one component in a series circuit fails, the entire circuit is broken.

Advantages: Simple to design and implement.; Easy to control total resistance by adding more resistors.

Disadvantages: Failure of one component leads to total circuit failure.; Current is limited by the total combined resistance.

Applications: String of decorative lights (e.g., fairy lights).; Current control in simple laboratory circuits.

Additional Info: In series circuits, $V_{	ext{total}} = V_1 + V_2$.. Option D represents the formula for resistors connected in parallel, where the reciprocal of the total resistance is the sum of the reciprocals: $\frac{1}{R_{	ext{eq}}} = \frac{1}{R_1} + \frac{1}{R_2}$.

Answer: C is correct — The total resistance in a series connection is the algebraic sum of the individual resistors, given by $R_{	ext{eq}} = R_1 + R_2$.

Exam Tip: Always verify if the question asks for 'series' or 'parallel'; 'series' involves addition, while 'parallel' involves reciprocals.

Examoogle · Answer

Option A: $R_1 	imes R_2$

Examoogle · Answer

Option B: $\frac{R_1}{R_2}$

Examoogle · Answer

Option D: $\frac{R_1 	imes R_2}{R_1 + R_2}$

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