# SCEN103 9/12 Notes

### Ohm's Law and Electrical Power

From "Batteries and Bulb" demonstation of Sept. 5, we found that current was directly proportional to voltage. What else controls how much current flows in a simple electrical circuit? The resistance!

### Ohm's Law:

So the slope of the line above is 1/R. [This follows from comparison of I=V/R and y=mx, a direct proportionality, where m is the slope or proportionality constant of the linear relationship (straight line).]

### Electrical Units:

All measurable quantities should be reported with units!

Voltage is measured in volts, V for short. Current is measured in amperes, amps for short, or A for shorter still. If voltage is measured in V and current is measured in A, then resistance as determined from Ohm's law (formula above) will have units of ohms, or "upper case omega" for short (from the Greek letter for "O").

Reconsidering the data from the graph above, we find that the slopes of the upper and lower curves are 0.299 A/V and 0.171 A/V, respectively. The reciprocal slope, which is R for each circuit, is 3.3 V/A and 5.8 V/A, respectively -- close to the 3 ohm and 6 ohm values that I mentioned.

### Schematics:

Actual circuits are usually represented by so-called schematics, where the functionality of each circuit element is represented, rather than its appearance.

The lines of different length in the battery schematic represent the stacks of dissimilar metals making up early batteries. The zig-zag lines represent the "tortuous" path that the charge carriers must traverse in passing through a resistor. Straight lines connecting circuit elements are connecting wires (sometimes referred to as leads) --- seldom shown as explicit components, but of great importance in forming the actual circuit.

The "+" on the battery symbol indicates the side of the battery with higher relative voltage and indicates the direction that current will flow when a single resistor is connected across it.

The circuit must be continuous to have flow, i.e. current. The switch must be closed for continuity; if switch is not closed, the circuit is said to be open -- no current flows.

"Water flows downhill." Fluid flows from high pressure to low pressure. The job of the pump is to force fluid back up to high pressure. In a similar way, a battery exerts "electrical pressure." A resistor is similar to a narrow pipe that would restrict flow.

### Electrical Energy:

A battery converts chemical energy to electrical energy. This conversion takes place at a certain rate -- the rate of energy conversion is known as the power delivered by the battery.

Energy delivered = (power) x (duration of delivery)

Electrical power is measured in units of watts (W). Utility companies charge us for the total energy delivered to us; they like to use kilowatt-hours (kW-hr) to measure the energy delivered. As a group exercise, you will be asked to estimate the cost of running a hairdryer for one hour. The power supplied by the battery depends on the voltage and current, directly proportional to both the pressure exerted and the rate of flow.

A resistor converts electrical enery into thermal energy (often referred to as heat). A lamp converts some of that energy into light. The rate at which a resistor dissipates energy is the power dissipated, and depends on the resistance and current in the following way:

Please note that this formula results from substitution of Ohm's law into P=I V.

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