Determine the magnitudes and directions of the currents in each resistor shown i

Question

Determine the magnitudes and directions of the currents in each resistor shown in the figure. The batteries have emfs of EMF_1 = 9.0V and Emf_2 = 11.7V and the resistors have values of R_1 = 28ohm , R_2 = 38ohm , and R_3 = 30ohm. A.) Ignore internal resistance of the batteries. find I1,I2,and I3 Express your answers using two significant figures. Enter your answers numerically separated by commas. B.)Assume each battery has internal resistance 1.5ohm. find I1, I2, and I3 Express your answers using two significant figures. Enter your answers numerically separated by commas.

Explanation / Answer

this may help you In a circuit involving one battery and a number of resistors in series and/or parallel, the resistors can generally be reduced to a single equivalent resistor. With more than one battery, the situation is trickier. If all the batteries are part of one branch they can be combined into a single equivalent battery. Generally, the batteries will be part of different branches, and another method has to be used to analyze the circuit to find the current in each branch. Circuits like this are known as multi-loop circuits. Finding the current in all branches of a multi-loop circuit (or the emf of a battery or the value of a resistor) is done by following guidelines known as Kirchoff's rules. These guidelines also apply to very simple circuits. Kirchoff's first rule : the junction rule. The sum of the currents coming in to a junction is equal to the sum leaving the junction. (Basically this is conservation of charge) Kirchoff's second rule : the loop rule. The sum of all the potential differences around a complete loop is equal to zero. (Conservation of energy) There are two different methods for analyzing circuits. The standard method in physics, which is the one followed by the textbook, is the branch current method. There is another method, the loop current method, but we won't worry about that one. The branch current method To analyze a circuit using the branch-current method involves three steps: Label the current and the current direction in each branch. Sometimes it's hard to tell which is the correct direction for the current in a particular loop. That does NOT matter. Simply pick a direction. If you guess wrong, you¹ll get a negative value. The value is correct, and the negative sign means that the current direction is opposite to the way you guessed. You should use the negative sign in your calculations, however. Use Kirchoff's first rule to write down current equations for each junction that gives you a different equation. For a circuit with two inner loops and two junctions, one current equation is enough because both junctions give you the same equation. Use Kirchoff's second rule to write down loop equations for as many loops as it takes to include each branch at least once. To write down a loop equation, you choose a starting point, and then walk around the loop in one direction until you get back to the starting point. As you cross batteries and resistors, write down each voltage change. Add these voltage gains and losses up and set them equal to zero. When you cross a battery from the - side to the + side, that's a positive change. Going the other way gives you a drop in potential, so that's a negative change. When you cross a resistor in the same direction as the current, that's also a drop in potential so it's a negative change in potential. Crossing a resistor in the opposite direction as the current gives you a positive change in potential.

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