Example Compute currents 𝐢𝟏and 𝐢𝟐in the circuit shown below. pD = v (7) = (−2) (7) = –W Apply KCL at each node and each supernode, using Ohm’s Law to express branch currents in terms of node voltages. The voltage and current of element C given in Figureadhere to the passive convention so. b) Apply KVL to relate the voltages of the nodes that form the supernodes) Solve the resulting simultaneous system of equations using substitution, calculator, Cramer’s Rule, etc) Use Ohm’s Law and node voltages to Superloop Equation (KVL): 𝐕𝐚𝐛𝐕𝐜𝐝𝐕𝐝𝐚𝟎 3 Notice that all the voltages and currents obey the sign convention!circuit is a collection of components and sources interconnected by “ideal wires”. We have too many unknowns to go further – the resistor voltages and the three currents are all unknown𝑖 1=𝑖2+𝑖−𝑣 1+𝑣 3+𝑣 4=0 −𝑣 3−𝑣 1+𝑣 2+𝑣 2=0 We KVL: −+−=VVwriteloop equation for each loop with a voltage not in the current set of equations. The power consumed by a device is always: The Kirchho ’s lawsa v vviVv IR iiviRviA B C E D * Kirchho ’s current law (KCL):P i k =at each node. b) Apply KVL to relate the voltages of the nodes that form the Let’s Do It: KCL and KVL But now what? − v – (−4) –=⇒ v = −2 V. The value of the current in element C in FigureisA. ⇒ Eliminate either V1 or I using Ohm’s Law eq: A: −+ + − =* Note that KCL is KCL, KVL, Energy Flow. Let us look at the following example to get familiar with writing superloop equations. e.g., at node B, i3 + i6 + i4 =(We have followed the convention that current leaving a node is positive.) bigger loop to solve the problem. Kirchhoff's Laws and Circuit Analysis (EC 2) Circuit analysis: solving for I and V at each element Linear circuits: involve resistors, capacitors, inductors Initial analysis uses only resistors Apply KCL at each node and each supernode, using Ohm’s Law to express branch currents in terms of node voltages. Note that since we still use a loop (just that it is bigger now), KVL holds! Sum of voltage drop around any loop of devices is always(KVL); sum of currents into any node is always(KCL). The objective of “circuit analysis” is to determine the voltage across each component and the current flowing through each component Apply Kirchhoff’s voltage law (KVL) to the loop consisting of elements C, D and B to get.
Example Compute currents 𝐢𝟏and 𝐢𝟐in the circuit shown below. pD = v (7) = (−2) (7) = –W Apply KCL at each node and each supernode, using Ohm’s Law to express branch currents in terms of node voltages. The voltage and current of element C given in Figureadhere to the passive convention so. b) Apply KVL to relate the voltages of the nodes that form the supernodes) Solve the resulting simultaneous system of equations using substitution, calculator, Cramer’s Rule, etc) Use Ohm’s Law and node voltages to Superloop Equation (KVL): 𝐕𝐚𝐛𝐕𝐜𝐝𝐕𝐝𝐚𝟎 3 Notice that all the voltages and currents obey the sign convention!circuit is a collection of components and sources interconnected by “ideal wires”. We have too many unknowns to go further – the resistor voltages and the three currents are all unknown𝑖 1=𝑖2+𝑖−𝑣 1+𝑣 3+𝑣 4=0 −𝑣 3−𝑣 1+𝑣 2+𝑣 2=0 We KVL: −+−=VVwriteloop equation for each loop with a voltage not in the current set of equations. The power consumed by a device is always: The Kirchho ’s lawsa v vviVv IR iiviRviA B C E D * Kirchho ’s current law (KCL):P i k =at each node. b) Apply KVL to relate the voltages of the nodes that form the Let’s Do It: KCL and KVL But now what? − v – (−4) –=⇒ v = −2 V. The value of the current in element C in FigureisA. ⇒ Eliminate either V1 or I using Ohm’s Law eq: A: −+ + − =* Note that KCL is KCL, KVL, Energy Flow. Let us look at the following example to get familiar with writing superloop equations. e.g., at node B, i3 + i6 + i4 =(We have followed the convention that current leaving a node is positive.) bigger loop to solve the problem. Kirchhoff's Laws and Circuit Analysis (EC 2) Circuit analysis: solving for I and V at each element Linear circuits: involve resistors, capacitors, inductors Initial analysis uses only resistors Apply KCL at each node and each supernode, using Ohm’s Law to express branch currents in terms of node voltages. Note that since we still use a loop (just that it is bigger now), KVL holds! Sum of voltage drop around any loop of devices is always(KVL); sum of currents into any node is always(KCL). The objective of “circuit analysis” is to determine the voltage across each component and the current flowing through each component Apply Kirchhoff’s voltage law (KVL) to the loop consisting of elements C, D and B to get.
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