1. Lecture 81 Single Loop Circuits and Voltage Division

2. Lecture 82 Single Loop Circuit A single loop circuit is one which has only a single loop. The same current flows through each element of the circuit-the elements are in series. We will consider circuits consisting of voltage sources and resistors.

3. Lecture 83 Example: Christmas Lights + - 120V 228  50 Bulbs Total 228  I

4. Lecture 84 Solve for I The same current I flows through the source and each light bulb-how do you know this? In terms of I, what is the voltage across each resistor? Make sure you get the polarity right! To solve for I, apply KVL around the loop.

5. Lecture 85 228I + 228I + … + 228I -120V = 0 I = 120V/(50  228  ) = 10.5mA + - 120V 228  I+- 228I + - + -

6. Lecture 86 Some Comments We can solve for the voltage across each light bulb: V = IR = 10.5mA 228  = 2.4V This circuit has one source and several resistors. The current is: Source voltage/sum of resistances (Series resistances sum)

7. Lecture 87 Example: Instrumentation + - v s (t) + - v n (t) RsRs + - v O (t) RIRI SensorAmplifier

8. Lecture 88 How to Find v O (t) Assign a current i(t). Assign voltages across the two resistors. Use Ohm’s law to express the voltages in terms of the current. Use KVL around the loop to get an equation for i(t). Use Ohm’s law to compute v O (t).

9. Lecture 89 How to Find v O (t) + - v s (t) + - v n (t) RsRs +- RIRI i(t) i(t) R s + - i(t) R I

10. Lecture 810 Apply KVL around the loop: i(t) R S + i(t) R I - v s (t) - v n (t) = 0 Solve for i(t): How to Find v O (t)

11. Lecture 811 Use Ohm’s law: How to Find v O (t)

12. Lecture 812 Some Comments The current i(t) is: sum of voltage sources/sum of resistors Two resistors in series form a voltage divider.

13. Lecture 813 Amplifier Input Resistance If R I is small relative to R S, what happens to v O (t)? If R I is large relative to R S, what happens to v O (t)? Which condition is preferable, and why?

14. Lecture 814 Voltage Division Consider two resistors in series with voltage v(t) across them: R1R1 R2R2 - v 1 (t) + + - v 2 (t) + - v(t)

15. Lecture 815 Suppose you have three resistors (R 1, R 2, and R 3 ) in series with a voltage v(t) across the series combination. What is the voltage v 1 (t) across R 1 ?

16. Lecture 816 Use voltage division to compute the voltage across a Christmas light bulb in a string of 60 identical bulbs. Assume an outlet voltage of 120V.