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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.

Consider the circuit shown in figure above. Suppose that \( i_A = 11 \text{ A}, \) \( i_B = 12 \text{ A}, \) \( V_A = 20 \text{ V} \) and \( V_B = 80 \text{ V}. \) Determine the sum of resistances \( R_1 \) and \( R_2. \)

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Determine the value of the current \( i \) in the circuit shown in figure above. Suppose that \( i_A= 4 \text{ A}, \) \( i_B = 1 \text{ A}, \) \( i_C = 3 \text{ A}, \) \( R_1 = 6 \ \Omega, \) \( R_2 = 2 \ \Omega, \) and \( R_3 = 4 \ \Omega. \)

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Consider the circuit shown in the above figure. The voltages across branches are given by \( V_A = 13 \text{ V}, \) \( V_C = 13 \text{ V}, \) \( V_D = 3 \text{ V}, \) \( V_E = -6 \text{ V}, \) and \( V_F = 16 \text{ V}. \) The currents flowing through branches are given by \( i_ A = 12 \text{ A}, \) \( i_C = 24 \text{ A}, \) \( i_D = 6 \text{ A}, \) \( i_E = -6 \text{ A}, \) and \( i_F = 6 \text{ A}. \) Find the values of the power supplied by branch \( B.\)

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Determine the current \( i \) in the circuit shown in figure above. Suppose that \( i_A = 24 \text{ A}, \) \( R_1 = 8 \ \Omega, \) \( R_2 = 4 \ \Omega, \) \( R_3 = 7 \ \Omega, \) and \( R_4 = 7 \ \Omega. \)

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Determine the value of the resistance \( R \) in the circuit shown in the figure above, given \( R_{eq} = 6 \ \Omega, \) \( R_1 = 4 \ \Omega, \) \( R_2 = 30 \ \Omega, \) \( R_3 = 24 \ \Omega, \) \( R_4 = 8 \ \Omega, \) \( R_5 = 3 \ \Omega, \) and \( R_6 = 1 \ \Omega. \)

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