Question

equivalent resistance of the circuit diagram is 6 ohm. calculate the value x.​

Answer 1

Answer :

Question :-

Equivalent resistance of the circuit diagram is 6 Ω . Calculate the value of x.

(See the attachment for the Circuit diagram)

To Find :-

The value of x resistor in the circuit.

Given :-

• Resistance between CD = 8 Ω

• Resistance between DE = 9 Ω

• Resistance between GH = 3 Ω

• Resistance between HI = 5 Ω

We know :-

Equivalent resistance in a Parallel Circuit :-

$\underline{\boxed{\bf{\dfrac{1}{R_{P}} = \dfrac{1}{R_{1}} + \dfrac{1}{R_{2}} + \dfrac{1}{R_{3}} + ... + \dfrac{1}{R_{n}}}}}$

Where :-

• R = Resistance of the circuit.

• $R_{p}$ = Equivalent resistance.

Equivalent resistance in a series circuit :-

$\underline{\boxed{\bf{R_{s} = R_{1} + R_{2} + R_{3} + ... + R_{n}}}}$

Where :-

• R = Resistance of the circuit.

• $R_{s}$ = Equivalent resistance.

Concept :-

According to diagram , the Resistance between C & F and G & I is in series circuit. While the resistance between CF and GI is in parallel circuit.

So first we will find the resistance of the resistors in series circuit and then we will use the formula and the given Equivalent resistance to find the required value.

Solution :-

⠀⠀⠀⠀⠀Resistance between C and F :-

Using the formula and substituting the values in it, we get :-

$:\implies \bf{R_{s} = R_{1} + R_{2} + R_{3}} \\ \\ \\ :\implies \bf{R_{s} = CD + DE + EF} \\ \\ \\ :\implies \bf{R_{s} = 8 + 9 + x} \\ \\ \\ :\implies \bf{R_{s} = 17 + x} \\ \\ \\ \therefore \purple{\bf{R_{s} = (17 + x)\:\Omega}}$

Hence, the Equivalent Resistance between C and F is (17 + x) Ω.

⠀⠀⠀⠀⠀ Resistance between C and F :-

Using the formula and substituting the values in it, we get :-

$:\implies \bf{R_{s} = R_{1} + R_{2}} \\ \\ \\ :\implies \bf{R_{s} = GH + HI} \\ \\ \\ :\implies \bf{R_{s} = 3 + 5} \\ \\ \\ :\implies \bf{R_{s} = 8} \\ \\ \\ \therefore \purple{\bf{R_{s} = 8\:\Omega}}$

Hence, the Equivalent Resistance between G and I is 8 Ω.

⠀⠀⠀⠀⠀⠀⠀⠀⠀To find the value of x :-

Using the formula and substituting the values in it, we get :-

$:\implies \bf{\dfrac{1}{R_{P}} = \dfrac{1}{R_{1}} + \dfrac{1}{R_{2}}} \\ \\ \\ :\implies \bf{\dfrac{1}{AB} = \dfrac{1}{CF} + \dfrac{1}{GI}} \\ \\ \\ :\implies \bf{\dfrac{1}{6} = \dfrac{1}{(17 + x)} + \dfrac{1}{8}} \\ \\ \\ :\implies \bf{\dfrac{1}{6} = \dfrac{8 + 17 + x}{(17 + x)8}} \\ \\ \\ :\implies \bf{\dfrac{1}{6} = \dfrac{25 + x}{136 + 8x}} \\ \\ \\ :\implies \bf{\dfrac{(136 + 8x)}{6} = 25 + x} \\ \\ \\ :\implies \bf{136 + 8x = 6(25 + x)} \\ \\ \\ :\implies \bf{136 + 8x = 150 + 6x} \\ \\ \\ :\implies \bf{8x - 6x = 150 - 136} \\ \\ \\ :\implies \bf{2x = 14} \\ \\ \\ :\implies \bf{x = 7} \\ \\ \\ \therefore \purple{\bf{x = 7\:\Omega}}$

Hence, the value of x is 7 Ω.

Answer 2

Explanation:

X=7

mark me as Brainlest