Given Circuit:

The given circuit consists of a current source I and three resistors R1, R2, and R3 connected in series. The circuit is connected between terminals a and b.

Analysis:

To find the Norton equivalent circuit between terminals a and b, we need to determine the Norton current source IN and the Norton resistance RN.

Norton Current Source (IN):

To find the Norton current source, we can first determine the current flowing through the circuit.

Using Ohm's Law, we can calculate the current flowing through the resistors R1, R2, and R3:

I1 = V/R1
I2 = V/R2
I3 = V/R3

Since the resistors are connected in series, the total current flowing through the circuit is the sum of the currents flowing through each resistor:

I = I1 + I2 + I3

Substituting the values of I1, I2, and I3:

I = V/R1 + V/R2 + V/R3
= V(1/R1 + 1/R2 + 1/R3)

Therefore, the Norton current source IN is equal to I.

Norton Resistance (RN):

To find the Norton resistance, we can calculate the equivalent resistance seen from terminals a and b.

The equivalent resistance is the sum of the resistances R1, R2, and R3:

RN = R1 + R2 + R3

Norton Equivalent Circuit:

The Norton equivalent circuit consists of a current source IN and a resistor RN connected in parallel.

The Norton current source IN is equal to the current flowing through the circuit, which is calculated as explained above.

The Norton resistance RN is equal to the sum of the resistances R1, R2, and R3.

Therefore, the Norton equivalent circuit between terminals a and b is a current source IN in parallel with a resistor RN.

Visually, the Norton equivalent circuit can be represented as:

```
IN
a o----[RN]----o b
```

where IN is the Norton current source and RN is the Norton resistance.

In summary, we have determined the Norton equivalent circuit between terminals a and b, which consists of a current source IN and a resistor RN in parallel. The Norton current source IN is equal to the current flowing through the circuit, and the Norton resistance RN is equal to the sum of the resistances R1, R2, and R3.