CourseNotes.30 - Figure 23: Three Resistors in Series with...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Figure 23: Three Resistors in Series with Their Simplified Equivalent Resistor Figure 24: Three Resistors in Parallel with Their Simplified Equivalent Resistor Next, we pass through the three resistors at each of which we lose iRi in potential. After that, we find ourselves back at point b and therefore V − iR1 − iR2 − iR3 = 0 ⇒ V = iR1 + iR2 + iR3 ⇒ V = i (R1 + R2 + R3 ) By comparing the last form of the expression with Ohm’s law, we can see what the resistance of our simplified resistor is. For n resistors in series, the equivalent simplified resistor is n Req = Rj (26) j =1 We now want to do the same thing, except for multiple resistors in parallel (see figure 24). In this case, we will use the fact that since opposite sides of each resistor are wired to opposite sides of the battery, the potential difference across each resistor must be the same. We will also use the fact noticed above that the sum of the currents through each resistor must be equal to the current flowing through the rest of the circuit (the battery in this case). i = i1 + i2 + i3 = V V V + + =V R1 R2 R3 1 1 1 + + R1 R2 R3 Or, rearranging V =i 1 1 R1 + 1 R2 + 1 R3 Hence, we see that (similar to capacitors in series) n resistors in parallel can be reduced to an equivalent resistor of resistance n 1 1 = (27) R eq j =1 R j 8.4 RC Circuits Up until now we have dealt with circuits which involve either capacitors of resistors but none which involve both at the same time. Lets consider this possibility now. The two situations which we will consider are: 1. The capacitor begins charged and is then allowed to discharge through a resistor. 2. The capacitor begins uncharged and is then charged by a battery through a resistor. Figure 25 illustrates how we could see both of these situations in one circuit. When the switch is in position a then the capacitor is charging through the resistor. When the switch is in position b the capacitor is discharging through the resistor. 30 ...
View Full Document

This note was uploaded on 12/05/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

Ask a homework question - tutors are online