Question

three resistors each of resistance 10 ohm are connected, in turn, to obtain a. minimum resistance b. maximum resistance. computer (a) the effective resistance in each case (b) the ratio of minimum to maximum resistance so obtained.​

Answer 1

the equivalent resistance is maximum when resistors are connected in series

$rs = 10 + 10 + 10 = 30 \: ohms$

the equivalent resistance is minimum when resistance is connected in parallel

$rp = \frac{10}{3} = 3.3 \: ohm$

the ratio of minimum to maximum resistance so obtained.

$\frac{rs}{rp} = \frac{30}{3.3} = 9.09 \:$

i hope this helps ( ╹▽╹ )

Answer 2

Answer:

a. For minimum resistance - connect in parallel

b. For maximum resistance - connect in series

(a) Effective maximum = 30 ohm and effective minimum = 3.33 ohm

(b) Ratio is 1 : 9

Explanation:

Three resistors each of resistance, R = 10 ohm

a. Resistors are connected in parallel to obtain the minimum resistance.

$\frac{1}{ R_{min}}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}$

⇒ $\frac{1}{R_{min}}=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}$

⇒ $\frac{1}{ R_{min}}=\frac{3}{10}$

⇒ $R_{min}=\frac{10}{3}$

⇒ $R_{min}=3.33$ ohm

b. Resistors are connected in series to obtain the maximum resistance.

$R_{max}}=R+R+R$

⇒ $R_{max}}=10+10+10$

⇒ $R_{max}}=30$ ohm.

(a) Effective resistance to get maximum resistance,

$R_{eff}=nR$, where $n$ is number of resistor

⇒ $R_{eff}=3 \cdot 10$

⇒ $R_{eff}=30$ ohm

Effective resistance to get minimum resistance,

$\frac{1}{ R_{eff}}=\frac{n}{R}$, where $n$ is number of resistor

⇒ $\frac{1}{ R_{eff}}=\frac{3}{10}$

⇒ $R_{eff}=\frac{10}{3}$

⇒ $R_{eff}=3.33$ ohm

(b) Ratio of minimum to maximum resistance,

Ratio = $\frac{R_{min}}{R_{max}}$

         = $\frac{10/3}{30}$

         = $\frac{1}{9}$

Thus, the ratio is 1:9.

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