Nuts and Volts - May/June 2018

the current that goes through both resistors by calculating the effective resistance. Since the 100 ohm resistor and the one million ohm resistor are in series, we can simply add them to determine what the effective resistance is to the circuit.

The same current will flow through both resistors:

1,000,000 + 100 = 1,000, 100 ohms Note that this is still very near one million ohms.

The current would then be: I = V / R = 10/1,000, 100 =

0.000009999 amps That’s pretty small. It’s a lot smaller than 0.1A we had before the “break.” Since the same small current flows through both resistors, we can calculate how much voltage drops across each resistor AND how much power will be dissipated by each resistor. Yes, the meter will dissipate power, just hopefully very little: V100 = I x R = 0.000009999 x

100 = 0.0009999 volts Power100 = V x I = 0.000000009998 watts The voltage across the 100 ohm resistor is now

0.0009999 volts. Not going to zap anybody here: V1000000 = I x R = 9.999 volts Power1000000 = I x R =

0.00009998 watts The voltage across the one million ohm resistor is now 9.999 volts. So, because the meter impedance is so high, the voltage across it is essentially the voltage source. We can also see here that a high resistance can result in the higher voltage. Sounds weird but it’s true.

Also note that the total power used by both resistors is far less than that used by the single 100 ohm resistor in the original circuit. Resistance goes up, voltage goes up, but power goes way down. Again, weird but true.

In reality, no voltmeter has an infinite impedance input. However, most of them are pretty high. Even a relatively inexpensive meter (the kind that are sometimes given free by certain stores) may have an input impedance of a million ohms — far higher than most devices in circuits we use every day.

Just in case there are some non-believers, here are some photos of me performing the experiment to show what happens.

In Figure 5, I’ve constructed the circuit placing my

May/June 2018 55

Got Two, Get Two Free

With Ohm's Law and the Power Equation, we have two formulas that provide an insignt as to what is happening with electrical systems — at least DC electrical systems.

Ohm's Law can be expressed in three ways: V = I x R, I = V/R, and R = V/I where V = voltage, R = resistance, and I = current.

If we know any algebra, we can see that each of these equations can give us the other two simply by solving for the value that we do not have.

The Power Equation is: P = V x I Wherever there is both voltage and current, there will be power going somewhere.

Using these two equations, we can get any two values given the other two. For example, assume that we know the voltage across and resistance of a device. The device may be anything. Knowing these two values, we can determine the other two: I = V/R Placing the voltage value for V and the resistance value for R, we have determined I (the current).