Current Electricity Charging Discharging Of Capacitors Question 135
Question: You are given several identical resistances each of value $ R=10,\Omega $ and each capable of carrying maximum current of 1 ampere. It is required to make a suitable combination of these resistances to produce a resistance of $ 5,\Omega $ which can carry a current of 4 amperes. The minimum number of resistances of the type $ R $ that will be required for this job
[CBSE PMT 1990]
Options:
A) 4
B) 10
C) 8
D) 20
Show Answer
Answer:
Correct Answer: C
Solution:
Suppose n resistors are used for the required job. Suppose equivalent resistance of the combination is R’ and according to energy conservation it’s current rating is $ i’. $ Energy consumed by the combination = n ´ (Energy consumed by each resistance)
Therefore $ i{{’}^{2}}R’=n\times i^{2}R $
Therefore $ n={{( \frac{i’}{i} )}^{2}}\times ( \frac{R’}{R} )={{( \frac{4}{1} )}^{2}}\times ( \frac{5}{10} )=8 $
BETA
