In series combination of resistances :

Options

A. p.d. is same across each resistance
B. total resistance is reduced
C. current is same in each resistance
D. all above are true.

Explanation

To solve the question regarding the series combination of resistances, let's analyze the statements one by one.

### Step-by-Step Solution:

1. **Understanding Series Combination**:
In a series combination, resistors are connected end-to-end, and the same current flows through each resistor. Let's denote the resistors as \( R_1 \) and \( R_2 \).

2. **Total Resistance in Series**:
The total or equivalent resistance \( R_{\text{net}} \) in a series circuit is calculated by simply adding the individual resistances:
\[ R_{\text{net}} = R_1 + R_2 \]
This means the total resistance is greater than any individual resistance.

3. **Potential Difference Across Each Resistor**:
According to Ohm's Law, the potential difference \( V \) across a resistor is given by:
\[ V = I \cdot R \]
In a series circuit, the total voltage \( V \) from the battery is divided among the resistors. The voltage across \( R_1 \) is:
\[ V_{R_1} = I \cdot R_1 \]
And the voltage across \( R_2 \) is:
\[ V_{R_2} = I \cdot R_2 \]
Since \( R_1 \) and \( R_2 \) are not necessarily equal, the potential difference across each resistor is not the same. Therefore, the first statement is **false**.

4. **Current in the Circuit**:
In a series circuit, the same current \( I \) flows through each resistor. The current can be calculated using the total voltage and total resistance:
\[ I = \frac{V}{R_{\text{net}}} = \frac{V}{R_1 + R_2} \]
Since the same current flows through both \( R_1 \) and \( R_2 \), the third statement is **true**.

5. **Conclusion on Total Resistance**:
The total resistance in a series combination is not reduced; it is increased. Therefore, the second statement is **false**.

### Summary of Results:
- **First Statement**: False (Potential difference is not the same across each resistance)
- **Second Statement**: False (Total resistance is increased)
- **Third Statement**: True (Current is the same in each resistor)

### Final Answer:
The only true statement regarding the series combination of resistances is that the current is the same in each resistor.

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