Resistors in Series Physics Notes

Resistors in Series →I is same Two resistors connected in series to a battery, ★ end A circuit diagram of the equivalent resistance of the two resistors in series, Req-R1+R2 end to I is same in both resistors A circuit diagram for the two resistors and battery. Figure 18.3 Two resistors, R₁ and R₂, in the form of incandescent light bulbs, in series with a battery. The currents in the resistors are the same, and the equivalent resistance of the combination is RRR like water flowing thru pipe AV = AV + AV2 IReqIR1+IR2 Req R1 + R2 + .... Resistors in Parallel PD is same. Two resistors connected in parallel to a battery A circuit diagram of the two resistors and battery A circuit diagram with equivalent resistance of the two parallel resistors b/c charge is conserved. ↑ I = 11+12 1 Ren R R I SPLITS 1 1 -+ 1 = Req R1 R2 + AV Reg AV AV R1 + R2 PROBLEM-SOLVING STRATEGY Simplifying Circuits with Resistors 1. Combine all resistors in series by summing the individual resistances and draw the new, simplified circuit diagram. Useful facts: Reg R₁Rg+Rg+ The current in each resistor is the same. 2. Combine all resistors in parallel by summing the reciprocals of the resistances and then taking the reciprocal of the result. Draw the new, simplified circuit diagram. Useful facts: -+ Req R R R + The potential difference across each resistor is the same. 3. Repeat the first two steps as necessary, until no further combinations can be made. If there is only a single battery in the circuit, the result will usually be a single equivalent resistor in series with the battery. 4. Use Ohm's law, AV = IR, to determine the current in the equivalent resis tor. Then work backwards through the diagrams, applying the useful facts listed in step 1 or step 2 to find the currents in the other resistors. (In more complex circuits, Kirchhoff's rules will be needed, as described in the next section.) Kirchhoff's Rules & Complex DC Circuits 1. The sum of the currents entering any junction must equal the sum of the currents leaving that junction. (This rule is often referred to as the june- tion rule.) 2. The sum of the potential differences across all the elements around any closed circuit loop must be zero. (This rule is usually called the loop rule.) PROBLEM-SOLVING STRATEGY Applying Kirchhoff's Rules to a Circuit 1. Assign labels and symbols to all the known and unknown quantities. 2. Assign directions to the currents in each part of the circuit. Although the assign- ment of current directions is arbitrary, you must stick with your original choices throughout the problem as you apply Kirchhoff's rules. 2. When applying the loop rule, you must choose a direction for traversing the loop and be consistent in going either clockwise or counterclockwise. As you traverse the loop, record voltage drops and rises according to the following rules (summarized in Fig. 18.14, where it is assumed that movement is from point a toward point b): (a) If a resistor is traversed in the direction of the current, the change in electric potential across the resistor is-IR (Fig. 18.14a). (b) If a resistor is traversed in the direction opposite the current, the change in electric potential across the resistor is +IR (Fig. 18.14b). (c) If a source of emf is traversed in the direction of the emf (from to + on the terminals), the change in electric potential is +E (Fig. 18.14c). (d) If a source of emf is traversed in the direction opposite the emf (from+toon the terminals), the change in electric potential is -E (Fig. 18.14d).