For any circuit, number of independent equations containing emf's, resistance and current equals:

Options

A. no. of junction
B. no. of branches
C. no. of branches + 1
D. no, of junction + number of branches

Explanation

To determine the number of independent equations containing EMFs, resistance, and current in any circuit, we can use the following steps:

### Step 1: Identify the Components of the Circuit
- **Junctions**: Points where two or more conductors meet.
- **Branches**: Paths in the circuit that can carry current.

### Step 2: Apply Kirchhoff's Laws
- **Kirchhoff's Current Law (KCL)** states that the total current entering a junction must equal the total current leaving the junction.
- **Kirchhoff's Voltage Law (KVL)** states that the sum of the electromotive forces (emfs) and the potential drops (voltage across resistors) in any closed loop of a circuit must equal zero.

### Step 3: Count the Junctions and Branches
- Let \( J \) be the number of junctions in the circuit.
- Let \( B \) be the number of branches in the circuit.

### Step 4: Determine the Number of Independent Equations
- The number of independent equations can be calculated using the formula:
\[ \text{Number of independent equations} = J + (B - 1) \]
This is derived from the fact that you can write \( J \) equations from KCL and \( B - 1 \) equations from KVL (since one loop can be derived from the others).

### Conclusion
Thus, the number of independent equations containing EMFs, resistance, and current in any circuit equals the number of junctions plus the number of branches minus one.