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Any circulating flow constitutes a circuit. Learn how to model the logic boards in your computer, the flow of nutrients in your blood, or the daily fluctuations in the temperature of your house.

The above circuit consists of resistors and a voltage source. If voltage source is given as \( V = 16 \text{ V} \) and the resistances are given as \( R_1 = 2 \Omega \) and \( R_2 = 4 \Omega,\) what is the current passing through the resistor \( R_1?\)

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Consider the circuit shown in the figure above. The voltages and currents are \[ v_2 = -2 \text{ V}, v_3 = 8 \text{ V}, v_6= 12 \text{ V}, i_3 = i_4 = i_5 = 4 \text{ A}. \] Determine the values of the voltage across the circuit element \( E. \)

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The above circuit consists of resistors and voltage sources. The voltages are given as \( V_1 = 32 \text{ V} \) and \( V_2 = 16 \text{ V}, \) and the resistances are given as \( R_1 = 2 \Omega, R_2 = 4 \Omega \) and \( R_3 = 6 \Omega. \) What is the voltage across the resistor \( R_3?\)

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In the above circuit, the voltage source gives \( V = 7 \text{ V}. \) When the resistance is given by \( R = 2 \Omega, \) what is the voltage \(V_R\) across the resistor?

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The above circuit consists of resistors and voltage sources. The voltage sources are given as \( V_1 = 90 \text{ V} \) and \( V_2 = 18 \text{ V}, \) and the resistances are given as \( R_1 = 3 \Omega, R_2 = 6 \Omega \) and \( R_3 = 9 \Omega. \) What is the current flow through the resistor \( R_3?\)

Assume that the ground is at the node under the voltage sources.

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