Predict the voltage of these?

In a circuit a rheostat(variable resistor) is being placed and a globe is being added. A 6v power supply is used. When the current is 0.2 A the voltage is 3.2v. Find the voltage when it's 0.1 A, 0.3 A, 0.4 A , 0.5 A.

Find the voltage when it's 0.1A, 0.3 A, 0.4A , 0.5 A when a wire is being used instead of a globe.

Answer:
Assuming the globe is not an inductive or capacitive load, the circuit equation is
(Voltage) = (Current) x (Resistance)

Since we have 3.2 V at 0.2 A, the circuit resistance (with globe and variable resistor set at "A") is 16 ohm.

To achieve different currents in the system, the variable resistor must be set to different values (since the globe is a constant resistance device). You've listed the currents, but not the corresponding resistor settings. Without these, you cannot calculate the required voltage.

Likewise, once a wire is used to replace the globe, you need to indicate the resistance of the wire itself in order to calculate applied voltages.
Actually it is not clear in you r question that the globe and rheostat are in series connection but lets assumed it is. Then
this voltage being measured is accross the globe only.

Voltage drop across the globe is, Vg = I x Rg
since the globe resistance is constant therefore the voltage drop is proportional to the current passing into it. Resistance value of the globe is R = 3.2/0.2 = 16 ohm

therefore the maximum current flows into the circuit is I = 6/16 = 0.375 A at rheostat resistance is 0 ohm.

for, 0.1A current voltage drop is 3.2x0.1 / 0.2 = 1.6 V
for , 0.3A voltage drop is 3.2x0.3/0.2 = 4.8 V
0.4A voltage drop is 3.2x0.4/0.2 = 6.4 V , not possible
0.5A is also not possible.

When the wire is use instead of globe assuming that wire resistance is so small almost equal to 0 ohm. Therefore the voltage drop is equal to 0 v. And the rheostat is absorbing all the load.
1. first of all the resistance of the rheostat is found by using the formula : V=IR, make R the subject and the equation becomes R=V/I using the two values given the resistance of the rheostat can be found to be 3.2V/0.2A =16 Ohms.
the voltages of the currents are therefore found by putting in the value of the resistance in the equation.
0.1A = 1.6V
0.3A = 4.8V
0.4A = 6.4V
0.5A = 8.0V

2. the voltages cannot be found because different wires have different resistances therefore the question would have to give more details than stated to answer it.
This is a trick question as the resistance of a globe varies according to the brightness of the filament and accordingly, the voltage across it at different currents will not be linear.
For instance, you may only need to increase the voltage one voltage and the brightness will increase dramatically, and the current will also increase by a large amount.

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