Constant Current Source Characteristics

A constant current source is an electronic circuit designed to deliver a steady, unvarying current to a load, regardless of changes in the load resistance or the voltage across the load. This characteristic holds true as long as the source operates within its specified compliance voltage limits.

Initial Current and Load Conditions

• The question states that the constant current source initially supplies a current of 400 mA.
• The initial load resistance is \(2 \, \text{k}\Omega\).

The critical information here is that the source is a "constant current source." This term directly implies that the current output will remain constant, even if the load connected to it changes.

Effect of Load Change on Current Source

When the load resistance is changed from \(2 \, \text{k}\Omega\) to \(200 \, \Omega\), a constant current source will maintain the same current output. According to Ohm's Law, \(V = I \times R\), the voltage across the load will adjust itself to accommodate the new resistance while keeping the current (I) constant. For example:

• Initially, with \(R_1 = 2 \, \text{k}\Omega = 2000 \, \Omega\) and \(I = 400 \, \text{mA} = 0.4 \, \text{A}\):
  \(V_1 = I \times R_1 = 0.4 \, \text{A} \times 2000 \, \Omega = 800 \, \text{V}\)
• After the load changes to \(R_2 = 200 \, \Omega\), the current \(I\) remains constant at 400 mA:
  \(V_2 = I \times R_2 = 0.4 \, \text{A} \times 200 \, \Omega = 80 \, \text{V}\)

As seen, the voltage across the load changes to maintain the constant current. The fundamental definition of a constant current source is that it strives to keep the current constant, irrespective of the load resistance, within its operational range.

Determining the New Load Current

Since the device is specified as a constant current source, its primary function is to deliver a fixed current. Therefore, even when the load resistance changes from \(2 \, \text{k}\Omega\) to \(200 \, \Omega\), the current supplied to the load will not change.

The load current will remain:

Load Current \( = 400 \, \text{mA}\)

Thus, the new load current will be 400 mA.