Kirchhoff's first law i.e. `sum I = 0` at a junction is based on the law of conservation of

Options

A. angular momentum
B. linear momentum
C. energy
D. charge

Answer

To solve the question regarding Kirchhoff's first law, we will follow these steps:

### Step 1: Understand Kirchhoff's First Law
Kirchhoff's first law states that the sum of currents entering a junction must equal the sum of currents leaving that junction. This can be mathematically expressed as:
\[ \sum I = 0 \]

### Step 2: Analyze the Currents at the Junction
Let’s assume we have a junction where:
- Current \( I_1 \) is entering the junction.
- Currents \( I_2 \) and \( I_3 \) are leaving the junction.

According to Kirchhoff's first law, we can write:
\[ I_1 - I_2 - I_3 = 0 \]

### Step 3: Rearranging the Equation
From the equation above, we can rearrange it to show the relationship between the currents:
\[ I_1 = I_2 + I_3 \]
This indicates that the current entering the junction (I1) is equal to the sum of the currents leaving the junction (I2 and I3).

### Step 4: Relate to Conservation Laws
The principle behind Kirchhoff's first law is based on the conservation of charge. This means that charge cannot be created or destroyed in an isolated system. Therefore, the total charge (and hence the current, which is the flow of charge) must remain constant at the junction.

### Conclusion
Thus, Kirchhoff's first law is based on the law of conservation of charge. The correct answer to the question is:
**Option D: Charge**

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