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--- 184_notes:r_parallel [2018/06/26 14:12] – [Loop Rule and Voltage in Parallel] curdemma
+++ 184_notes:r_parallel [2020/08/23 20:20] – dmcpadden
@@ Line 1: / Line 1: @@
 Sections 19.2 and 19.3 in Matter and Interactions (4th edition)
-[[184_notes:c_series|Next Page: Capacitors in Series]]
+/*[[184_notes:kirchoffs_rules|Next Page: Using Loop and Node Rules to Solve a Circuit]]
-[[184_notes:r_series|Previous Page: Resistors in Series]]
+[[184_notes:r_series|Previous Page: Resistors in Series]]*/
 ===== Resistors in Parallel =====
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 {{youtube>BKelyviRRwE?large}}
 ==== Node Rule and Current in Parallel ====
-[{{  184_notes:Week8_7.png?300|Current $I$ breaks into two different currents, $I_1$ and $I_2$ at the node in this circuit}}]
+[{{  184_notes:Week8_7.png?300|Current $I$ breaks into two different currents, $I_1$ and $I_2$ at the top node in this circuit}}]
-When two circuit elements are parallel, this means that there are two different paths along the circuit that take you across the same potential difference. For example, consider a circuit with a battery and two resistors (similar to before), but this time there is a split in the wire and the resistors are side-by-side rather than in a row. When we use the node rule, on the this circuit, there are two nodes that are of particular interest (Points A and B in the circuit diagram). The node rule says that the current going into a node should be the same as the current leaving the node to satisfy conservation of charge. For Point A, this means that current from the battery is split when it hits the branches for the $R_1$ and $R_2$ resistors, but **//the sum of the current in each branch should be equal to the total current coming from the battery//**. This is a different mathematical statement of conservation of charge than we had for series elements, but still quite powerful.
+When two circuit elements are parallel, this means that there are two different paths along the circuit that take you across the same potential difference. For example, consider a circuit with a battery and two resistors (similar to before), but this time there is a split in the wire and the resistors are side-by-side rather than in a row. When we use the node rule, on the this circuit, there are two nodes that are of particular interest (the points where there are three wires coming together in the circuit diagram). The node rule says that the current going into a node should be the same as the current leaving the node to satisfy conservation of charge. For the top node, this means that current from the battery is split when it hits the branches for the $R_1$ and $R_2$ resistors, but **//the sum of the current in each branch should be equal to the total current coming from the battery//**. This is a different mathematical statement of conservation of charge than we had for series elements, but still quite powerful.
 $$I_{bat}=I_1+I_2$$
@@ Line 34: / Line 34: @@
 ==== Equivalent Resistance ====
-{{ 184_notes:Week8_9.png?500}}
+[{{ 184_notes:Week8_9.png?500|Circuit with resistors in parallel, $R_1$ and $R_2$, and its equivalent circuit with $R_e$}}]
 To simplify parallel circuits, we will again try to replace the resistors in parallel with a single resistor that has an equivalent resistance. We will still do this by comparing a circuit with two resistors in parallel to a circuit with a single equivalent resistor, keeping the $\Delta V_{bat}$ and $I_{bat}$ the same for both circuits. From the node rule in the two-resistor circuit, we know that: