Question

Resistors R1, and R2 have an equivalent resistance
of 6 ohms when connected in the circuit shown
below. The resistance of R1 could be in
(1) 1
(2) 5
(3) 8
(4) 4​

Answer 1

Answer:

3) 8

Explanation:

because

equivalent resistor of parallel series

is smaller than the resistor

8>6

Answer 2

The resistance of R₁ is 8 ohm.

(3) is correct option

Explanation:

Given that,

Resistors R1, and R2 have an equivalent resistance  of 6 ohms.

The eqivalent resistance is

$\dfrac{R_{1}R_{2}}{R_{1}+R_{2}}=6\ \Omega$

We need to calculate the value of R₂

Using equation (I)

$\dfrac{R_{1}R_{2}}{R_{1}+R_{2}}=6\ \Omega$

If the value of R₁ is 1 ohm

Put the value of R₁

$\dfrac{R_{2}}{1+R_{2}}=6\ \Omega$

$R_{2}=6+6R_{2}$

$R_{2}=-\dfrac{6}{5}\ \Omega$

It is not possoble.

If the value of R₁ is 5 ohm

Put the valye in the equation (I)

$\dfrac{5R_{2}}{5+R_{2}}=6\ \Omega$

$R_{2}=-30\ \Omega$

It is not possoble.

If the value of R₁ is 8 ohm

Put the valye in the equation (I)

$\dfrac{8R_{2}}{8+R_{2}}=6\ \Omega$

$R_{2}=24\ \Omega$

It is possoble.  

If the value of R₁ is 4 ohm

Put the valye in the equation (I)

$\dfrac{4R_{2}}{4+R_{2}}=6\ \Omega$

$R_{2}=-12\ Omega$

It is not possoble.  

Hence, The resistance of R₁ is 8 ohm.

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Topic : resistance

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