What is the highest and lowest total resistan | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given four coils with resistances $R_1 = 4 \,\Omega, R_2 = 8 \,\Omega, R_3 = 12 \,\Omega$,and $R_4 = 24 \,\Omega$.$(a)$ To obtain the highest tota

Vedclass · Accepted Answer

$48 \,\Omega; 2 \,\Omega$

Vedclass · Answer

(A) Given four coils with resistances $R_1 = 4 \,\Omega, R_2 = 8 \,\Omega, R_3 = 12 \,\Omega$,and $R_4 = 24 \,\Omega$.$(a)$ To obtain the highest total resistance,the coils must be connected in series. The equivalent resistance $R_s$ is the sum of individual resistances:$R_s = R_1 + R_2 + R_3 + R_4 = 4 + 8 + 12 + 24 = 48 \,\Omega$.$(b)$ To obtain the lowest total resistance,the coils must be connected in parallel. The equivalent resistance $R_p$ is given by:$\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4} = \frac{1}{4} + \frac{1}{8} + \frac{1}{12} + \frac{1}{24}$.Taking the least common multiple $(LCM)$ of $4, 8, 12, 24$,which is $24$:$\frac{1}{R_p} = \frac{6 + 3 + 2 + 1}{24} = \frac{12}{24} = \frac{1}{2}$.Therefore,$R_p = 2 \,\Omega$.Thus,the highest resistance is $48 \,\Omega$ and the lowest resistance is $2 \,\Omega$.

What is the highest and lowest total resistance that can be secured by combinations of four coils of resistance $4 \,\Omega, 8 \,\Omega, 12 \,\Omega$ and $24 \,\Omega$?

Similar Questions

What is meant by equivalent resistance?

Two identical resistors,each of resistance $2 \Omega$,are connected in turn: $(i)$ in series,and $(ii)$ in parallel to a battery of $12 \text{ V}$. Calculate the ratio of power consumed in the two cases.

$A$ battery of $9 \, V$ is connected in series with resistors of $0.2 \, \Omega$,$0.3 \, \Omega$,$0.4 \, \Omega$,$0.5 \, \Omega$,and $12 \, \Omega$ respectively. How much current (in $A$) would flow through the $12 \, \Omega$ resistor?

$(a)$ What is the total resistance of $n$ resistors each of resistance $R$ connected in:
$(i)$ series?
$(ii)$ parallel?
$(b)$ Calculate the resultant resistance of $3$ resistors $3 \ \Omega, 4 \ \Omega$,and $12 \ \Omega$ connected in parallel.

Two wires of the same metal have the same length, but cross-sections are in the ratio $3 : 1$. They are joined in series. The resistance of the thicker wire is $10\, \Omega$. The total resistance of the combination will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module