Question

The equivalent resistance of two resistors connected in parallel is 7.2 ohm and if one resistance is 12 ohm. Find the value of other?​

Answer 1

Answer:

18 ohms

Explanation:

Given :

• Equivalent resistance of two resistors connected in parallel = 7.2 ohms

• Resistance of the first resistor = 12 ohms

To find :

• Value of the resistance of the other resistor (x)

As they are connected in parallel :

1/7.2 = 1/12 + 1/x

1/72/10 = 1/12 + 1/x

10/72 = 1/12 + 1/x

1/x = 10/72-1/12

1/x = 10/72 - 6/72

1/x = 4/72

x = 72/4

x = 18 ohms

The value of resistance of other resistor is 18 ohms

Answer 2

Given :

• The equivalent resistance of two resistors connected in parallel is 7.2 ohm
• One of the resistor is of resistance 12 ohm

To Find :

• Value of the resistance of other resistor

Solution :

According to the question ...

They are connected in parallel , so from the formula —

$\qquad\underline{ \fbox{ \sf{ \dfrac{1}{R} = \dfrac{1}{R_{1}} + \dfrac{1}{R_{2}} }}} \\ \\ \longrightarrow \: \sf{ \dfrac{1}{7.2} = \dfrac{1}{12} + \dfrac{1}{R_{2}} } \\ \\ \longrightarrow \: \sf{ \dfrac{1}{R_{2}} = \dfrac{1}{7.2} - \dfrac{1}{12} } \\ \\ \longrightarrow \: \sf{ \dfrac{1}{R_{2}} = \dfrac{10}{72} - \dfrac{1}{12} } \\ \\ \longrightarrow \: \sf{ \dfrac{1}{R_{2}} = \dfrac{10 - 6}{72} } \\ \\ \longrightarrow \: \sf{ \dfrac{1}{R_{2}} = \dfrac{4}{72} } \\ \\ \longrightarrow \: \sf{ R_{2} = \dfrac{72}{4}} \\ \\ \longrightarrow \: \sf \red{{ R_{2} = 18 \: ohm }}$

So, the value of resistance of other resistor is 18 ohms