In a potentiometer of 10 wires, the balance point is obtained on the `7^(th)`. To shift the balance point to `9^(th)` wire, we should

Options

A. decrease resistance in the main circuit.
B. increase resistance in the main circuit.
C. decrease resistance in series the cell whose emf is to be measured.
D. increase resistance in series with the cell whose emf is to be determined

Explanation

To solve the problem of shifting the balance point from the 7th wire to the 9th wire in a potentiometer with 10 wires, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Potentiometer**: A potentiometer is used to measure the potential difference between two points in a circuit. It consists of a long wire or multiple wires connected in series. The balance point indicates where the potential difference is equal to the EMF being measured.

2. **Current and Balance Point Relationship**: The balance point is directly related to the EMF and the potential gradient of the potentiometer wire. The potential gradient is defined as the potential difference per unit length of the wire.

3. **Current Decrease to Shift Balance Point**: To shift the balance point from the 7th wire to the 9th wire, we need to increase the balancing length. This implies that the EMF must increase relative to the potential gradient. Since the potential gradient is inversely proportional to the current, we need to decrease the current in the circuit.

4. **Increasing Resistance**: To decrease the current, we can increase the resistance in the circuit. According to Ohm's law (V = IR), if we increase the resistance (R) while keeping the voltage (V) constant, the current (I) will decrease.

5. **Connecting Resistance in Series**: The resistance should be connected in series with the potentiometer wire where the EMF is being measured. This will effectively increase the total resistance in the circuit, thereby reducing the current and decreasing the potential gradient.

6. **Conclusion**: By increasing the resistance in series with the potentiometer, we can shift the balance point from the 7th wire to the 9th wire.

### Final Answer:
To shift the balance point to the 9th wire, we should **increase the resistance in series with the potentiometer.**

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