6.3 Variational Analysis

This is the third section of Module 6 in the Navy Basic Electricity and Electronics series, a module on parallel circuits. The sections so far are:

6.1 Rules for Voltage and Current
6.2 Rules for Resistance and Power

This third section is about how voltage, current, power, and total resistance change as voltage is increased or resistance is increased/decreased.

1. So the basic principles so far in this module are that

• Voltage is going to be the same in every branch of a parallel circuit.
• Total current is the sum of the current in every branch.
• The total resistance goes down if you add another branch.
• E = IR
• P = EI

So this section plays out a few scenarios.

2. What if you double the voltage from the source?

• Voltage in every branch will go up.
• Therefore, current in every branch will go up because I = E/R.
• Resistance will stay the same--it's a physical factor.
• Power will go up because P = EI.

3. What if you add another resistor in another branch?

• Voltage remains the same in every branch.
• There will now be current in that branch and since current is additive, the total current will go up.
• That means the total power will go up, since P = EI.
• Total resistance will go down, due to the reciprocal method.

4. What if you change the resistance in one branch, say decreasing it?

• Voltage remains the same in every branch.
• Current goes up in that branch because I = E/R.
• Therefore, total current goes up.
• Therefore, total power goes up.
• Since R_total = E/I and total current goes up, total resistance goes down.