Question

three resistance each of 4 ohms are connected to form a triangle . the Resistance between any two terminals is ???????????????

Answer 1

The Resistance between any two terminals is $R=\dfrac{8}{3}$ohms.

Explanation:

Given,

The three resistance (R) = 4 ohms

To find, the Resistance between any two terminals = ?

The two  resistance are connected in series

$=R_{1}+R_{2}$

= 4 + 4 = 8 ohms

The two  resistance are connected in parallel ( 8 ohms and 4 ohms)

$\dfrac{1}{R}=\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}$

⇒ $\dfrac{1}{R}=\dfrac{{R_{1}}+{R_{2}}}{R_{1}{R_{2}}}$

⇒ $R=\dfrac{{R_{1}}{R_{2}}}{R_{1}+{R_{2}}}$

⇒ $R=\dfrac{8\times 4}{8+4}=\dfrac{32}{12}$

⇒ $R=\dfrac{8}{3}$ ohms

Hence, the Resistance between any two terminals is $R=\dfrac{8}{3}$ ohms.

Answer 2

The Resistance between any two terminals is 2.66 ohms .

Explanation:

• Three resistances are joined together in form of a triangle.
• Now two points in this circuit of triangle is considered to calculate the equivalent resistance.
• When any two points are considered when two resistances will come in series and the other resistance will be in parallel so calculating as per the circuit given value of resistance = 4 ohm .

Series:

4+4 = 8 ohms

Now the parallel,

                                        $\frac{1}{4} + \frac{1}{8} = \frac{1}{ER}$

              ER (equivalent resistance)= $\frac{8}{(2+1)}$

                                                = $\frac{8}{3}$  

= 2.66 ohms .

To know more:

Three resistance each of 8 ohm are connected to a triangle. the resistance between any two terminal Will be ?

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