The figure shows a circuit having eight resistances of $1 Ω$ each, labelled $R_{1}$ to $R_{8}$ , and two ideal batteries with voltages $ε_{1} = 12 V$ and $ε_{2} = 6 V$ . [2022]

Which of the following statement(s) is(are) correct

Question

The figure shows a circuit having eight resistances of $1 Ω$ each, labelled $R_{1}$ to $R_{8}$ , and two ideal batteries with voltages $ε_{1} = 12 V$ and $ε_{2} = 6 V$ . [2022]

Which of the following statement(s) is(are) correct?

Smart Achievers · Accepted Answer

(1, 2, 3, 4)

Here we have folding symmetry, so circuit can be redrawn as

By mesh analysis:

In circuit ACO

$0.5 i_{1} + 0.5 (i_{1} - i_{2}) + i_{1} - 6 = 0$

$0.5 i_{1} + 0.5 i_{1} - 0.5 i_{2} + i_{1} - 6 = 0$

$2 i_{1} - 0.5 i_{2} = 6$

$8 i_{1} - 2 i_{2} = 24 \dots (i)$

In circuit ADO

$0.5 i_{2} + 1 \times i_{2} - 12 + 0.5 (i_{2} - i_{1}) = 0$

$2 i_{2} - 0.5 i_{1} = 12 \dots (i i)$

From (i) and (ii), we get

$7.5 i_{1} = 36$

$i_{1} = \frac{36}{7.5} = 4.8 A$

So, current through $' R_{1}' = i_{1} = 4.8 A$

$Putting i_{1} = 4.8 A in (ii), we get$

$2 i_{2} - 2.4 = 12$

$2 i_{2} = 14.4$ $\Rightarrow i_{2} = 7.2 A$ $\Rightarrow Current through R_{1} = 7.2 A$

$So, current through R_{2} = \frac{| i_{2} - i_{1} |}{2} = \frac{| 7.2 - 4.8 |}{2} = 1.2 A$

$Current through R_{5} = \frac{i_{1}}{2} = \frac{4.8}{2} = 2.4 A$

Solution

Q.
The figure shows a circuit having eight resistances of $1 Ω$ each, labelled $R_{1}$ to $R_{8}$ , and two ideal batteries with voltages $ε_{1} = 12 V$ and $ε_{2} = 6 V$ . [2022]

Which of the following statement(s) is(are) correct

1 The magnitude of current flowing through $R_{1}$ is 7.2 A.

2 The magnitude of current flowing through $R_{2}$ is 1.2 A.

3 The magnitude of current flowing through $R_{3}$ is 4.8 A.

4 The magnitude of current flowing through $R_{5}$ is 2.4 A.

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Solution

Q. The figure shows a circuit having eight resistances of 1Ω each, labelled R1 to R8, and two ideal batteries with voltages ε1=12V and ε2=6V. [2022] Which of the following statement(s) is(are) correct

1 The magnitude of current flowing through R1 is 7.2 A.

2 The magnitude of current flowing through R2 is 1.2 A.

3 The magnitude of current flowing through R3 is 4.8 A.