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**Lakhmir Singh Physics Class 10 Solutions ****Page No:43**

**Question 43:**

Show with the help of diagrams, how you would connect three resistors each of resistance 6 Î©, so that the combination has resistance of (i) 9 Î© (ii) 4 Î©.**Solution :**

Resultant resistance for parallel circuit=R

1/R = 1/6 + 1/6

1/R = 2/6 R = 3

Effective resistance = 6 + 3 = 9ohms

Resultant resistance for each parallel circuit= R

1/R = 1/6+1/6+1/6

1/R = 3/6

R = 2

Therefore effective resistance = 2+2 = 4ohms.

**Question 44:**

Two resistances when connected in parallel give resultant value of 2 ohm; when connected in series the value becomes 9 ohm. Calculate the value of each resistance.**Solution :**

Two resistances when connected in series, resultant value is 9ohms.

Two resistances when connected in parallel, resultant value is 2ohms.

Let the two resistances be R_{1} and R_{2}.

If connected in series, then

9 = R_{1+ }R_{2}

R_{1} = 9-R_{2}

If connected in parallel, then

1/2 = 1/R_{1}+1/R_{2}

From above equations we get that

1/2=(R_{1+}R_{2})/R_{1}R_{2}

1/2 = 9/(9-R_{2}) R_{2}

9R_{2}-R_{2}^{2 }= 18

R_{2}^{2}-9R_{2}+18 = 0

(R_{2}-6) (R_{2}-3)=0

R_{2} = 6,3

So if R_{2} = 6ohms, then R_{1 }= 9-6 =3ohms.

If R_{2} = 3ohms, then R_{1}= 9-3 = 6ohms.

**Question 45:**

A resistor of 8 ohms is connected in parallel with another resistor X. The resultant resistance of the combination is 4.8 ohms. What is the value of the resistor X ?**Solution :**

Given:

A resistor of 8ohm is connected in parallel with a resistor of X.

And resultant is 4.8.

Then X = ?

We know that for parallel case

1/R = 1/R1+1/X

1/4.8 = 1/8+1/x

1/4.8 - 1/8 = 1/x

After solving we get that

X = 12ohms

**Question 46:**

You are given three resistances of 1,2 and 3 ohms. Show by diagrams, how with the help of these resistances you can get:

(i) 6 Î© (ii) [latex s=2]\frac{6}{11}[/latex] Î© (iii) 1.5 Î©**Solution :**

Equivalent resistance = 10 + 20 + 30 = 60

Equivalent resistance

Equivalent resistance of first line = 1Î© + 2Î© = 3Î©

Resistance of the second line = 3 0 Equivalent resistance

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