Oregon State University PH 213, Class #16 Figure 30.20A Figure 30.20A 5/8/17 Oregon State University PH 213, Class #16

Oregon State University PH 213, Class #16 Ohm’s Law The “height” from which charge “falls” is a voltage difference, V. The path by which charge falls is a conductor—any material that allows charge to flow freely. The rate at which an amount of charge, q, flows past any point in a conductor, q/t, is called the electric current, I, and it’s measured in coulombs/sec, or Amperes (A). The ratio of the voltage difference, V, to the resulting current, I, is called the resistance, R, a definition known as Ohm’s law: V/I = R or V = IR R has units of ohms (). 5/8/17 Oregon State University PH 213, Class #16

Oregon State University PH 213, Class #16 Resistors in Series A resistor is the reason for voltage drop in a circuit. It’s the site of “loss” of some of the potential energy of the charge flowing—tapped by some device for work or heat (or both). For every such resistor linked in series (one after another) in a circuit, the voltage drop across it is given by V = IR. Since the sum of all these voltage drops must be the total voltage drop, VT, around the circuit (all the way from the high side to the low side of the voltage source), this means: V = VT = V1 + V2 + V3 .... = IR1 + IR2 + IR3... = I(R1 + R2 + R3...) That is, we can replace all those individual resistors in series with a single resistor RS whose value is the sum of the individual R- values. 5/8/17 Oregon State University PH 213, Class #16

Internal Resistance of a Voltage Source A battery or a generator or any other device that creates a constant voltage source has a little bit of resistance in its own materials—a value denoted as r. So the true voltage the device offers at its working terminals is usually slightly less than “rated.” How much less? That depends on the current it is delivering, because the voltage drop across any resistance is the product of the resistance value times the current flowing through that resistance. Example: A car battery has an internal resistance of about 0.01 . Note how that affects the terminal voltage if I = 10 A, or 100 A, etc. 5/8/17 Oregon State University PH 213, Class #16

The Energy Flow (Power) of an Electric Current The potential energy change of a given amount of charge, q, “falling” is given by: UE = qV Therefore, the rate at which that potential energy is converted (the power) is given by: P = qV/t And so, for a voltage difference (“height”) that doesn’t change with time, the steady power is given by: P = V(q/t) = VI But since V/R = I (that is, V = IR), we have several ways to write the power of such a steady-state current flow: P = V(I) P = (V)2/R P = I2·R 5/8/17 Oregon State University PH 213, Class #16

Oregon State University PH 213, Class #16 You have two identical space heaters, each of which will produce 1000 W of heat output when plugged into your wall outlet indi-vidually. But then you connect them in series and plug this combi-nation into your wall outlet. What is their total power output now? 1. 500 W 2. 1000 W 3. 2000 W 4. 1414 W 5. None of the above. (Always draw a picture of the circuit—it helps!) 5/8/17 Oregon State University PH 213, Class #16

VT/RT = VT/R1 + VT/R2 + VT/R3.... 1/RT = 1/R1 + 1/R2 + 1/R3.... Resistors in Parallel A resistor is called that because it impedes current flow. The more resistance you place into the one path of a charge flow, the slower the current will be. But what if you offer the current more than one path—with a resistance in each such path? That actually increases the total current; even if the second path is “equally slow,” you’re still allowing twice as much current to flow as before. Adding another parallel resistor decreases the overall resistance of the circuit, because it increases the overall current of the circuit: IT = I1 + I2 + I3.... VT/RT = VT/R1 + VT/R2 + VT/R3.... 1/RT = 1/R1 + 1/R2 + 1/R3.... 5/8/17 Oregon State University PH 213, Class #16

Oregon State University PH 213, Class #16 Example: Find the total resistance of a set of three resistors, connected in parallel: R1 = 5 W R2 = 10 W R3 = 10 W 5/8/17 Oregon State University PH 213, Class #16

Simplifying Multiple-Resistor Circuits Sometimes, circuits can be modeled with simpler versions— arrange-ments that carry the same total current via fewer resistors. You can do this modeling by using the rules for series and parallel resistors. Example: Find the total power dissipated in this circuit by modeling it as one equivalent resistance: A 15 V battery with a 1/4  internal resistance is connected to two parallel branches. In the first branch, there is just a 19 resistor. In the second branch there is a 5 resistor in series with two other parallel resistors, 2 and 4. 1. 30.0 W 2. 45.0 W 3. 60.0 W 4. 75.0 W 5. None of the above. 5/8/17 Oregon State University PH 213, Class #16