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Kirchhoff's Junction Law

The given fou...

Question

The given four terminal network is part of a larger circuit. The points $A, B, C$ are at the same potential. The potential difference between any one of $A, B$ or $C$ and $D$ is $40 V$ . The potential difference between $A$ and $O$ is

10 V

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15 V

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18 V

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20 V

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Solution

The correct option is A $10 V$
According to Kirchhoff's Junction Law:

$I_{C O} + I_{B O} + I_{A O} = I_{O D}$

$\Rightarrow \frac{V_{C} - V_{O}}{R} + \frac{V_{B} - V_{O}}{R} + \frac{V_{A} - V_{O}}{R} = \frac{V_{O} - V_{D}}{R}$
$(∵ V_{A} = V_{B} = V_{C})$

$\Rightarrow 3 (\frac{V_{A} - V_{O}}{R}) = \frac{V_{O} - V_{A} + V_{A} - V_{D}}{R}$

$\Rightarrow 3 (\frac{V_{A} - V_{O}}{R}) = - (\frac{V_{A} - V_{O}}{R}) + (\frac{V_{A} - V_{D}}{R})$

$\Rightarrow 4 (\frac{V_{A} - V_{O}}{R}) = \frac{V_{A} - V_{D}}{R}$

$\Rightarrow 4 (V_{A} - V_{O}) = 40$

$\Rightarrow V_{A} - V_{O} = 10 V$

Hence, the correct answer is (A).

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The given four terminal network is part of a larger circuit. The points A,B,C are at the same potential. The potential difference between any one of A,B or C and D is 40 V. The potential difference between A and O is

The correct option is A 10 VAccording to Kirchhoff's Junction Law: ICO+IBO+IAO=IOD ⇒VC−VOR+VB−VOR+VA−VOR=VO−VDR (∵VA=VB=VC) ⇒3(VA−VOR)=VO−VA+VA−VDR ⇒3(VA−VOR)=−(VA−VOR)+(VA−VDR) ⇒4(VA−VOR)=VA−VDR ⇒4(VA−VO)=40 ⇒VA−VO=10 V Hence, the correct answer is (A).

The given four terminal network is part of a larger circuit. The points $A, B, C$ are at the same potential. The potential difference between any one of $A, B$ or $C$ and $D$ is $40 V$ . The potential difference between $A$ and $O$ is