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Using Kirchhoff's Current Law, determine the value of current I in the given circuit diagram.

Physics

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Answer

D\text{D}

Step-by-step solution

4 steps

To find the value of current II, we will apply Kirchhoff's Current Law (KCL) at each junction in the circuit diagram. KCL states that the sum of currents entering a junction must equal the sum of currents leaving that junction.

  1. Apply KCL at the first junction (leftmost).

    Two currents, 3 A and 1.5 A, are entering this junction. Let the current leaving this junction be I1I_1.

    I1=3 A+1.5 AI_1 = 3 \text{ A} + 1.5 \text{ A} I1=4.5 AI_1 = 4.5 \text{ A}
  2. Apply KCL at the second junction (where I1I_1 splits).

    Current I1I_1 (4.5 A) is entering this junction. Current 0.5 A is leaving, and another current, let's call it I2I_2, is also leaving.

    I1=0.5 A+I2I_1 = 0.5 \text{ A} + I_2 4.5 A=0.5 A+I24.5 \text{ A} = 0.5 \text{ A} + I_2 I2=4.5 A−0.5 AI_2 = 4.5 \text{ A} - 0.5 \text{ A} I2=4.0 AI_2 = 4.0 \text{ A}
  3. Apply KCL at the third junction (where I2I_2 and 2.5 A meet).

    Current I2I_2 (4.0 A) and 2.5 A are entering this junction. Let the current leaving this junction be I3I_3.

    I3=I2+2.5 AI_3 = I_2 + 2.5 \text{ A} I3=4.0 A+2.5 AI_3 = 4.0 \text{ A} + 2.5 \text{ A} I3=6.5 AI_3 = 6.5 \text{ A}
  4. Apply KCL at the fourth junction (final junction where I3I_3 splits into II and 1.5 A).

    Current I3I_3 (6.5 A) is entering this junction. Currents II and 1.5 A are leaving this junction.

    I3=I+1.5 AI_3 = I + 1.5 \text{ A} 6.5 A=I+1.5 A6.5 \text{ A} = I + 1.5 \text{ A} I=6.5 A−1.5 AI = 6.5 \text{ A} - 1.5 \text{ A} I=5.0 AI = 5.0 \text{ A}

    The calculated value for II is 5.0 A.
    Comparing this with the given options:
    [A] 0.3 A
    [B] 0.5 A
    [C] 1.3 A
    [D] इनमें से कोई नहीं (None of these)

    Since 5.0 A is not among options A, B, or C, the correct option is [D].

    The final answer is D\text{D}.

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