What is the highest and lowest total resistan | vedclass

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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 $24 \,\Omega$?

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