[amp_mcq option1=”9 times” option2=”$$\frac{1}{9}$$ times” option3=”$$\frac{1}{3}$$ times” option4=”3 times” correct=”option3″]
The correct answer is: C. $\frac{1}{3}$ times
When three identical resistors are connected in parallel, the equivalent resistance is given by:
$$R_{eq} = \frac{R}{3}$$
When three identical resistors are connected in series, the equivalent resistance is given by:
$$R_{eq} = 3R$$
Therefore, the resultant resistance of the first combination to the second is:
$$\frac{R}{3} \div 3R = \frac{1}{3}$$
Explanation of each option:
- Option A: 9 times. This is incorrect because the resultant resistance of the first combination is $\frac{R}{3}$, which is 1/3 of the resistance of the second combination.
- Option B: $\frac{1}{9}$ times. This is incorrect because the resultant resistance of the first combination is $\frac{R}{3}$, which is 3 times the resistance of the second combination.
- Option C: $\frac{1}{3}$ times. This is the correct answer because the resultant resistance of the first combination is $\frac{R}{3}$, which is 1/3 of the resistance of the second combination.
- Option D: 3 times. This is incorrect because the resultant resistance of the first combination is $\frac{R}{3}$, which is 1/3 of the resistance of the second combination.