Two batteries of difference emf's and internal resistance are connected in parallel to one another.

Options

A. Equivalent emf will be grater than either of the emf's
B. Equivalent emf will be smaller than either of the emf
C. Equivalent internal resistance will be grater than either of the two internal resistances
D. Equivalent internal resistance will be smaller than either of the two internal resistances.

Explanation

To solve the problem of two batteries with different EMFs and internal resistances connected in parallel, we will analyze the situation step by step.

### Step 1: Identify the parameters of the batteries
Let’s denote the EMFs and internal resistances of the two batteries as follows:
- Battery 1: EMF = E1, Internal Resistance = R1
- Battery 2: EMF = E2, Internal Resistance = R2

### Step 2: Understand the configuration
The two batteries are connected in parallel. In a parallel connection, the voltage across each battery is the same, and the total current flowing through the circuit is the sum of the currents from each battery.

### Step 3: Analyze the equivalent EMF
When two batteries are connected in parallel, the equivalent EMF (E_eq) is determined by the battery with the higher EMF. However, the actual voltage across the terminals will be affected by the internal resistances and the current flowing through the circuit.

Using Kirchhoff's Voltage Law (KVL), we can express the voltage across the terminals:
- For Battery 1: \( V = E1 - I \cdot R1 \)
- For Battery 2: \( V = E2 - I \cdot R2 \)

Since both batteries are in parallel, the voltage across them must be equal:
\[ E1 - I1 \cdot R1 = E2 - I2 \cdot R2 \]

### Step 4: Determine the equivalent EMF
To find the equivalent EMF, we note that the current will flow from the battery with the higher EMF to the one with the lower EMF. Therefore, if E1 > E2, the equivalent EMF will be less than E1 and E2 due to the voltage drop across the internal resistances.

Thus, we can conclude:
- The equivalent EMF (E_eq) will be less than the higher EMF (E1 or E2).

### Step 5: Analyze the equivalent internal resistance
The equivalent internal resistance (R_eq) of two resistors in parallel is given by the formula:
\[ R_{eq} = \frac{R1 \cdot R2}{R1 + R2} \]

This formula shows that the equivalent resistance will always be less than either of the individual resistances (R1 or R2).

### Conclusion
From our analysis, we can summarize:
1. The equivalent EMF (E_eq) will be less than either of the individual EMFs (E1 or E2).
2. The equivalent internal resistance (R_eq) will be less than either of the internal resistances (R1 or R2).

### Final Answer
- The equivalent EMF is less than either of the two EMFs.
- The equivalent internal resistance is smaller than either of the two internal resistances.