Question

Calculate the resistance between X and Y.​

Answer 1

Answer:

The resistance between X and Y is 7Ω.

Explanation:

As per the provided information in the given question, we have :

• $\sf { R_1 }$ = 4Ω
• $\sf { R_2 }$ = 4Ω
• $\sf { R_3 }$ = 12Ω

We are asked to calculate the equivalent resistance between X and Y.

Here,

$\sf {( R_2) }$ and $\sf {(R_3 )}$ are in parallel combination (Fig 1). Let's first calculate the combined resistance of $\sf {( R_2) }$ and $\sf {(R_3 )}$ .

Equivalent resistance in the parallel combination in given by,

$\\ \longrightarrow \quad \pmb{\boxed{\sf {\dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dots \dfrac{1}{R_n} }} }$

Substituting the values,

$\\ \longrightarrow \sf{\quad {\dfrac{1}{R_{(2,3)} } = \dfrac{1}{4} + \dfrac{1}{12} }}$

$\\ \longrightarrow \sf{\quad {\dfrac{1}{R_{(2,3)} } = \dfrac{3 + 1}{12} }}$

$\\ \longrightarrow \sf{\quad {\dfrac{1}{R_{(2,3)} } = \dfrac{4}{12} }}$

On reciprocating both sides,

$\\ \longrightarrow \sf{\quad {R_{(2,3)}= \dfrac{12}{4} }}$

$\\ \longrightarrow \bf{\quad \underline{R_{(2,3)}= 3 \; \Omega }}$

Now, the combined resistance of $\sf {( R_2) }$ and $\sf {(R_3 )}$ will become a single resistance of 3Ω. Also, $\sf {( R_1) }$ and $\sf {(R_{(2,3)} )}$ are in series combination now. (Fig 2)

Resultant resistance in series combination is given by,

$\\ \longrightarrow \quad \pmb{\boxed{\sf {R_S= R_1 + R_2 + \dots R_n}} }$

Substituting values,

$\\ \longrightarrow \sf{\quad { R_{(1,2,3)} = R_1 + R_{(2,3)} }}$

$\\ \longrightarrow \sf{\quad { R_{(1,2,3)} = (4 + 3) \; \Omega }}$

$\\ \longrightarrow \bf{\quad \underline { R_{(1,2,3)} = 7 \; \Omega }}$

Therefore, the resistance between X and Y is 7Ω.

Answer 2

Answer:it is 7 ohm

Explanation:

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