Physics

Physics

Problem

41. When two resistors, having resistance

R_{1}

and

R_{2}

, are connected in parallel, the equivalent resistance of the combination is

5 \,\Omega

. Which of the following statements about the resistances is correct? (A) Both

R_{1}

and

R_{2}

are greater than

5 \,\Omega

. (B) Both

R_{l}

and

R_{2}

are equal to

5 \,\Omega

. (C) Both

R_{1}

and

R_{2}

are less than

5 \,\Omega

. (D) One of the resistances is greater than

5 \,\Omega

, one of the resistances is less than

5 \,\Omega

. (A) Both

R_{1}

and

R_{2}

are greater than

5 \,\Omega

. (B) Both

R_{l}

and

R_{2}

are equal to

5 \,\Omega

. (C) Both

R_{1}

and

R_{2}

are less than

5 \,\Omega

. (D) One of the resistances is greater than

5 \,\Omega

, one of the resistances is less than

5 \,\Omega

.

Intuitive explanation

Parallel resistance combines reciprocals: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$ . The key insight is that adding positive reciprocals always gives a larger reciprocal than either individual one, which means the equivalent resistance must be smaller than both individual resistances. Think of it as current having multiple paths—it always finds an easier way through, lowering the total resistance.

Intuitive explanation

Parallel resistance combines reciprocals: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$ . The key insight is that adding positive reciprocals always gives a larger reciprocal than either individual one, which means the equivalent resistance must be smaller than both individual resistances. Think of it as current having multiple paths—it always finds an easier way through, lowering the total resistance.

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