Three resistors are joined together across a 24 Volts battery (see the figure).

Question

Three resistors are joined together across a 24 Volts battery (see the figure). The voltage drop across resistor R1 is 5.849 Volts, the current i2 through resistor R2 is 0.193 A, and the power dissipated in resistor R3 is 3.526 W. What is the value of each resistor? R1? R2? R3? What is the current through each resistor? i1? i3? What is the power dissipated in each resistor? P1? P2? Find the total resistance of the network. Find the current drawn from the battery. Find the total power used by the circuit

Explanation / Answer

Voltage across r1 = 5.849 V so voltage across r2, r3 = 24-5.849 v = 18.151 V so current through R3 = 3.526/18.151 = i3 = .194 A Current through r1 = i1 = i2 + i3 = .387 A Voltage across r2 = 18.151 v so r2 = 18.151/.193 = 94.05 ohm resitance r3 = 18.151/.194 = 93.56 ohm r1 = V1/i1 = 5.849/.387 = 15.11 ohm P1 = i1^2*r1 = 2.264 W P2 = i2^2*r2 = 3.502 W Total power used by circuit = P1 + P2 + P3 = 9.292 W Total resistance = r1 + (r2 parallel r3) = 62.01 ohm Current drawn = i1 = .387 A

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