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Announcementsp Homework for tomorrow…
(Ch. 22, Hmwk Set 22.3)1) a) identical currents b) stays the same2) a) 1.0 x 10-5 C b) 4.2 x 10-3 A3) a) 1.9 x 1019
4) 4A up, 2A down, 1A up
p Office hours…MW 2-3 pmTF 11-12 pmR 9-10 am
p Tutorial Learning Center (TLC) hours:M 8-5 R 8-1, 2-8T 11-8 F 9-11, 1-3W 8-7 SU 1-6
Chapter 22
Current and Resistance(Ohm’s Law and Resistor Circuits)
p The potential difference across a wire…
p Current through a wire…
p Resistance of a wire…
Last time…
�Vwire = �Vbat<latexit sha1_base64="9U5+GETd2ndFaI1/+4HgFlm37xk=">AAACHnicbVBNS8NAEN3Ur1q/qh69LBbBU0lFtB6Egh48VrAf0ISy2W7bpZtN2J2oIeSfePGvePGgInjSf+O2zUHbPhh4vDfDzDwvFFyDbf9YuaXlldW1/HphY3Nre6e4u9fUQaQoa9BABKrtEc0El6wBHARrh4oR3xOs5Y2uxn7rninNA3kHcchcnwwk73NKwEjd4plzzQQQ3OwmDnAZO74XPCYPXLE0vVzoeQTStFss2WV7AjxPKhkpoQz1bvHL6QU08pkEKojWnYodgpsQBZwKlhacSLOQ0BEZsI6hkvhMu8nkvxQfGaWH+4EyJQFP1L8TCfG1jn3PdPoEhnrWG4uLvE4E/aqbcBlGwCSdLupHAkOAx2HhnsmBgogNIVRxcyumQ6IIBRNpwYRQmX15njROyhdl+/a0VKtmaeTRATpEx6iCzlEN3aA6aiCKntALekPv1rP1an1Yn9PWnJXN7KN/sL5/AbB1pDU=</latexit><latexit sha1_base64="9U5+GETd2ndFaI1/+4HgFlm37xk=">AAACHnicbVBNS8NAEN3Ur1q/qh69LBbBU0lFtB6Egh48VrAf0ISy2W7bpZtN2J2oIeSfePGvePGgInjSf+O2zUHbPhh4vDfDzDwvFFyDbf9YuaXlldW1/HphY3Nre6e4u9fUQaQoa9BABKrtEc0El6wBHARrh4oR3xOs5Y2uxn7rninNA3kHcchcnwwk73NKwEjd4plzzQQQ3OwmDnAZO74XPCYPXLE0vVzoeQTStFss2WV7AjxPKhkpoQz1bvHL6QU08pkEKojWnYodgpsQBZwKlhacSLOQ0BEZsI6hkvhMu8nkvxQfGaWH+4EyJQFP1L8TCfG1jn3PdPoEhnrWG4uLvE4E/aqbcBlGwCSdLupHAkOAx2HhnsmBgogNIVRxcyumQ6IIBRNpwYRQmX15njROyhdl+/a0VKtmaeTRATpEx6iCzlEN3aA6aiCKntALekPv1rP1an1Yn9PWnJXN7KN/sL5/AbB1pDU=</latexit><latexit sha1_base64="9U5+GETd2ndFaI1/+4HgFlm37xk=">AAACHnicbVBNS8NAEN3Ur1q/qh69LBbBU0lFtB6Egh48VrAf0ISy2W7bpZtN2J2oIeSfePGvePGgInjSf+O2zUHbPhh4vDfDzDwvFFyDbf9YuaXlldW1/HphY3Nre6e4u9fUQaQoa9BABKrtEc0El6wBHARrh4oR3xOs5Y2uxn7rninNA3kHcchcnwwk73NKwEjd4plzzQQQ3OwmDnAZO74XPCYPXLE0vVzoeQTStFss2WV7AjxPKhkpoQz1bvHL6QU08pkEKojWnYodgpsQBZwKlhacSLOQ0BEZsI6hkvhMu8nkvxQfGaWH+4EyJQFP1L8TCfG1jn3PdPoEhnrWG4uLvE4E/aqbcBlGwCSdLupHAkOAx2HhnsmBgogNIVRxcyumQ6IIBRNpwYRQmX15njROyhdl+/a0VKtmaeTRATpEx6iCzlEN3aA6aiCKntALekPv1rP1an1Yn9PWnJXN7KN/sL5/AbB1pDU=</latexit>
I =�Vwire
R<latexit sha1_base64="pTpnzz2AdxxVd4/TDqhMrkNAR7M=">AAACD3icbVC7SgNBFJ31GeMramkzGESrsBHBWAgBLbSLYh6QXcLsZDYZMju7zNxVl2U/wcZfsbFQsbW182+cPApNPDBwOOde7pzjRYJrsO1va25+YXFpObeSX11b39gsbG03dBgryuo0FKFqeUQzwSWrAwfBWpFiJPAEa3qD86HfvGNK81DeQhIxNyA9yX1OCRipUzi4OnN8RWjqXDABBDc6qQNcJk7ghQ/pPVcsy7L0JusUinbJHgHPkvKEFNEEtU7hy+mGNA6YBCqI1u2yHYGbEgWcCpblnViziNAB6bG2oZIETLvpKFCG943SxX6ozJOAR+rvjZQEWieBZyYDAn097Q3F/7x2DH7FTbmMYmCSjg/5scAQ4mE7uGsCUxCJIYQqbv6KaZ+YfsB0mDcllKcjz5L6Uem0ZF8fF6uVSRs5tIv20CEqoxNURZeohuqIokf0jF7Rm/VkvVjv1sd4dM6a7OygP7A+fwBuq52u</latexit><latexit sha1_base64="pTpnzz2AdxxVd4/TDqhMrkNAR7M=">AAACD3icbVC7SgNBFJ31GeMramkzGESrsBHBWAgBLbSLYh6QXcLsZDYZMju7zNxVl2U/wcZfsbFQsbW182+cPApNPDBwOOde7pzjRYJrsO1va25+YXFpObeSX11b39gsbG03dBgryuo0FKFqeUQzwSWrAwfBWpFiJPAEa3qD86HfvGNK81DeQhIxNyA9yX1OCRipUzi4OnN8RWjqXDABBDc6qQNcJk7ghQ/pPVcsy7L0JusUinbJHgHPkvKEFNEEtU7hy+mGNA6YBCqI1u2yHYGbEgWcCpblnViziNAB6bG2oZIETLvpKFCG943SxX6ozJOAR+rvjZQEWieBZyYDAn097Q3F/7x2DH7FTbmMYmCSjg/5scAQ4mE7uGsCUxCJIYQqbv6KaZ+YfsB0mDcllKcjz5L6Uem0ZF8fF6uVSRs5tIv20CEqoxNURZeohuqIokf0jF7Rm/VkvVjv1sd4dM6a7OygP7A+fwBuq52u</latexit><latexit sha1_base64="pTpnzz2AdxxVd4/TDqhMrkNAR7M=">AAACD3icbVC7SgNBFJ31GeMramkzGESrsBHBWAgBLbSLYh6QXcLsZDYZMju7zNxVl2U/wcZfsbFQsbW182+cPApNPDBwOOde7pzjRYJrsO1va25+YXFpObeSX11b39gsbG03dBgryuo0FKFqeUQzwSWrAwfBWpFiJPAEa3qD86HfvGNK81DeQhIxNyA9yX1OCRipUzi4OnN8RWjqXDABBDc6qQNcJk7ghQ/pPVcsy7L0JusUinbJHgHPkvKEFNEEtU7hy+mGNA6YBCqI1u2yHYGbEgWcCpblnViziNAB6bG2oZIETLvpKFCG943SxX6ozJOAR+rvjZQEWieBZyYDAn097Q3F/7x2DH7FTbmMYmCSjg/5scAQ4mE7uGsCUxCJIYQqbv6KaZ+YfsB0mDcllKcjz5L6Uem0ZF8fF6uVSRs5tIv20CEqoxNURZeohuqIokf0jF7Rm/VkvVjv1sd4dM6a7OygP7A+fwBuq52u</latexit>
R =⇢L
A<latexit sha1_base64="FE8NSqzq9fphVPojN2rRRvbBHmM=">AAAB+nicbVBNS8NAEJ3Ur1q/Yj16WSyCp5KIYD0IFS8ePFQxttCUstlu2qWbbNjdiCXkr3jxoOLVX+LNf+O2zUGrDwYe780wMy9IOFPacb6s0tLyyupaeb2ysbm1vWPvVu+VSCWhHhFcyE6AFeUspp5mmtNOIimOAk7bwfhy6rcfqFRMxHd6ktBehIcxCxnB2kh9u3p77ocSk8yXI4Gu8+wi79s1p+7MgP4StyA1KNDq25/+QJA0orEmHCvVdZ1E9zIsNSOc5hU/VTTBZIyHtGtojCOqetns9hwdGmWAQiFNxRrN1J8TGY6UmkSB6YywHqlFbyr+53VTHTZ6GYuTVNOYzBeFKUdaoGkQaMAkJZpPDMFEMnMrIiNsotAmrooJwV18+S/xjutndefmpNZsFGmUYR8O4AhcOIUmXEELPCDwCE/wAq9Wbj1bb9b7vLVkFTN78AvWxzcC8pPx</latexit><latexit sha1_base64="FE8NSqzq9fphVPojN2rRRvbBHmM=">AAAB+nicbVBNS8NAEJ3Ur1q/Yj16WSyCp5KIYD0IFS8ePFQxttCUstlu2qWbbNjdiCXkr3jxoOLVX+LNf+O2zUGrDwYe780wMy9IOFPacb6s0tLyyupaeb2ysbm1vWPvVu+VSCWhHhFcyE6AFeUspp5mmtNOIimOAk7bwfhy6rcfqFRMxHd6ktBehIcxCxnB2kh9u3p77ocSk8yXI4Gu8+wi79s1p+7MgP4StyA1KNDq25/+QJA0orEmHCvVdZ1E9zIsNSOc5hU/VTTBZIyHtGtojCOqetns9hwdGmWAQiFNxRrN1J8TGY6UmkSB6YywHqlFbyr+53VTHTZ6GYuTVNOYzBeFKUdaoGkQaMAkJZpPDMFEMnMrIiNsotAmrooJwV18+S/xjutndefmpNZsFGmUYR8O4AhcOIUmXEELPCDwCE/wAq9Wbj1bb9b7vLVkFTN78AvWxzcC8pPx</latexit><latexit sha1_base64="FE8NSqzq9fphVPojN2rRRvbBHmM=">AAAB+nicbVBNS8NAEJ3Ur1q/Yj16WSyCp5KIYD0IFS8ePFQxttCUstlu2qWbbNjdiCXkr3jxoOLVX+LNf+O2zUGrDwYe780wMy9IOFPacb6s0tLyyupaeb2ysbm1vWPvVu+VSCWhHhFcyE6AFeUspp5mmtNOIimOAk7bwfhy6rcfqFRMxHd6ktBehIcxCxnB2kh9u3p77ocSk8yXI4Gu8+wi79s1p+7MgP4StyA1KNDq25/+QJA0orEmHCvVdZ1E9zIsNSOc5hU/VTTBZIyHtGtojCOqetns9hwdGmWAQiFNxRrN1J8TGY6UmkSB6YywHqlFbyr+53VTHTZ6GYuTVNOYzBeFKUdaoGkQaMAkJZpPDMFEMnMrIiNsotAmrooJwV18+S/xjutndefmpNZsFGmUYR8O4AhcOIUmXEELPCDwCE/wAq9Wbj1bb9b7vLVkFTN78AvWxzcC8pPx</latexit>
§ A battery is a source of potential difference DVbat.
§ The battery creates a potential difference DVwire = DVbat between the ends of the wire.
§ The potential difference in the wire DVwire generates an E-field in the wire.
§ The E-field establishes a current, I.§ The current in the wire is determined
jointly by the battery and the wire’s resistance, R, to be:
p I = DVwire/R
Resistance and Ohm’s Law
Notice: Ohm’s Law is NOT a Law!The materials to which Ohm’s law applies are called Ohmic.p i.e.’s: metals and conductors
Resistance and Ohm’s Law
The current through a wire is measured as the potential difference DV is varied. What is the wire’s resistance?
1. 0.01 W.2. 0.02 W.3. 50 W.4. 100 W.5. Some other value.
Quiz Question 1
When you press the lever on a toaster, a switch connects the heating wires to 120 V. The wires are initially cool, but the current in the wire raises the temperature until they are hot enough to glow. As the wire heats up, how does the current in the toaster change?
Conceptual i.e. 22.9:The changing current in a toaster
How does the voltage drop across the resistors compare to the voltage drop across the wires?
A simple circuit…
Q: How does the voltage drop across the wires compare to the voltage drop across the resistor?
A: ΔVwire << ΔVresist
Resistance and Ohm’s Law
p The E-field in a resistor carrying a current is uniform.n The strength of the E-field is…
The E-field
E =�V
L
<latexit sha1_base64="ilJ8ioAjBu71BAPb+4Zxrx0pPMM=">AAAB/XicbVDLSsNAFJ34rPUVHzs3g0VwVRIp2I1QUMGFiwr2AU0pk+mkHTqZhJkboYbgr7hxoYhb/8Odf+O0zUJbD1w4nHMv997jx4JrcJxva2l5ZXVtvbBR3Nza3tm19/abOkoUZQ0aiUi1faKZ4JI1gINg7VgxEvqCtfzR5cRvPTCleSTvYRyzbkgGkgecEjBSzz68vvACRWjqXTEBBDez9Dbr2SWn7EyBF4mbkxLKUe/ZX14/oknIJFBBtO64TgzdlCjgVLCs6CWaxYSOyIB1DJUkZLqbTq/P8IlR+jiIlCkJeKr+nkhJqPU49E1nSGCo572J+J/XSSCodlMu4wSYpLNFQSIwRHgSBe5zxSiIsSGEKm5uxXRITBhgAiuaENz5lxdJ86zsVsqVu0qpVs3jKKAjdIxOkYvOUQ3doDpqIIoe0TN6RW/Wk/VivVsfs9YlK585QH9gff4A9CGU4g==</latexit>
A 15 Ω resistor is connected to the terminals of a 1.5 V battery. a) Draw a graph showing the potential as a function of
distance traveled through the circuit, starting from V = 0 V at the negative terminal of the battery.
b) What is the current in the circuit?
i.e. 22.10:Analyzing a single-resistor circuit
A thermistor is a device whose resistance varies with temperature in a well-defined way. A certain thermistor has a resistance of 2.8 kΩ at 20ºC and 3.9 kΩ at 70ºC. This thermistor is used in a water bath in a lab to monitor the temperature. The thermistor is connected in a circuit with a 1.5 V battery, and the current is measured. What is the change in current in the circuit as the temperature rises from 20ºC to 70ºC?
i.e. 22.11:Using a thermistor
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