Question

The circuit shown in the figure below is connected for 2.70 min. (Assume R = 3.40 , R2 - 1.40 81, and V = 17.0 V.) w 5.000 3.000 1.00 4.00 V (a) Determine the current in each branch of the circuit. branch magnitude (A) direction left branch middle branch right branch ---SE... v Select (b) Find the energy delivered by each battery. 4.00 V battery 3 17.0 V battery (c) Find the energy delivered to each resistor. 8.40 L resistor 5.00 resistor 1.00 resistor 3.00. resistor 1.40 Sl resistor (d) Identify the type of energy storage transformation that occurs in the operation of the circuit. This answer has not been graded yet. (e) Find the total amount of energy transformed into internal energy in the resistors.

Answer 1

(a) From the current i be the current through left loop and iz be the current through right loop, iz Be the current through Rz Applying Kirchhoff's second law around the left side loop 4-614 -iz) – 8.41 = 0 4-6i +6i2 – 8.41 = 0 4-14.4i, +61 = =0- ---(1) Applying Kirchhoff's second law around the right side loop 17-6(iz – 1 ) -5i, = 17+61, -1li, = 0 ---(2) From the junction rule, is = iz – 1 ---(3) By solving the equation, i =1.0193 A in = 2.196 A iz =1.003 A (b) The energy delivered by the 4.0 V batteries is, E31 = Vit = (4.0)(1.0193)(2.70(60)) = 660.51J The energy delivered by the 17.0 V batteries is, Ex2 =Vizt = (17.0)(2.196)(2.70(60)) =6047.78 J (c) The energy delivered to a 8.4022 resistor is, E6.89 = 1;?Rt =(1.0193)°(8.40)(2.70(60)) =1413.83 J The energy delivered to a 5.00 22 resistor is, E3.00 =iz{Rt =(1.003)? (5.0)(2.70(60)) =814.87 J The energy delivered to a 1.00 resistor is,

E.02 =(iz – 1) Rt =(1.003) (1.0)(2.70 (60)) =162.97 J The energy delivered to a 3.00 22 resistor is, E3.00 = izRt = (2.196)? (3.0)(2.70 (60)) = 2343.69 J The energy delivered to a 1.40 2. resistor is, E1.602 = iz Rt = (2.196)' (1.40)(2.70(60)) =1093.72 J (d) Chemical to heat transformation occurs in the operation of the circuit. (0) The total internal energy stored in the resistor is, E =1413.83+814.87 +162.97 +2343.69+1093.72 = 5829.1 J =5.83 kJ