# What is the relationship between the current and the

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What is the relationship between the current and the voltage through a resistor ? ANSWER: Hint 4. Apply Kirchhoff's loop rule: Finish the Kirchhoff's loop rule equation for the circuit with the battery, ammeter, and resistor . Express the voltage in terms of the resistance and the current . ANSWER: Hint 5. Apply Kirchhoff's loop rule: Finish the Kirchhoff's loop rule equation for the circuit with the battery, ammeter, resistor , and one resistor . Express the voltage in terms of the resistances and and the current , which is the same through each resistor. ANSWER: Hint 6. Apply Kirchhoff's loop rule: Finish the Kirchhoff's loop rule equation for the circuit with the battery, ammeter, a resistor with resistance , and two resistors with resistance . Express the voltage in terms of the resistances and and the current , which is the same through each resistor. ANSWER: Hint 7. Finding a relation between and Using the information and equations for and in terms of , , and , find a relation between and . Express your answer numerically. ANSWER: ANSWER: Correct The current through each resistor in a given circuit is the same. The current through each successive resistor in the series decreases. = = = = = 4 = 0.667
5/4/14 Ch19Hw: Current , Resistance and Direct Current Circuits 5/29 session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2772094 Kirchhoff's Rules and Applying Them Learning Goal: To understand the origins of both of Kirchhoff's rules and how to use them to solve a circuit problem. This problem introduces Kirchhoff's two rules for circuits: Kirchhoff's loop rule : The sum of the voltage changes across the circuit elements forming any closed loop is zero. Kirchhoff's junction rule : The algebraic sum of the currents into (or out of) any junction in the circuit is zero. The figure shows a circuit that illustrates the concept of loops , which are colored red and labeled loop 1 and loop 2. Loop 1 is the loop around the entire circuit, whereas loop 2 is the smaller loop on the right. To apply the loop rule you would add the voltage changes of all circuit elements around the chosen loop. The figure contains two junctions (where three or more wires meet)­­they are at the ends of the resistor labeled . The battery supplies a constant voltage , and the resistors are labeled with their resistances. The ammeters are ideal meters that read and respectively. The direction of each loop and the direction of each current arrow that you draw on your own circuits are arbitrary. Just assign voltage drops consistently and sum both voltage drops and currents algebraically and you will get correct equations. If the actual current is in the opposite direction from your current arrow, your answer for that current will be negative. The direction of any loop is even less imporant: The equation obtained from a counterclockwise loop is the same as that from a clockwise loop except for a negative sign in front of every term (i.e., an inconsequential change in overall sign of the equation because it equals zero).