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In the circuit diagram shown on the right, let I_1, I_2, I_3 and I_4 represent t

ID: 1413423 • Letter: I

Question

In the circuit diagram shown on the right, let I_1, I_2, I_3 and I_4 represent the current in each of the resistors, R_1, R_2, R_3 and R_4 respectively. The voltage of the battery. Delta V, remains constant. How does the current in each resistor with the switch open compare with the current in that same resistor with the switch closed? (Insert the appropriate sign: ) If R_1 = 20 Ohm, R_2 = 40 Ohm, R_3 = 60 Ohm, R_4 = 120 Ohm and Delta V = 80 V, then what do I_1, I_2, 1_3 and I_4 equal when the switch is closed? A copper wire has a length of 7.54 m, and a diameter of 0.400 mm. The resistivity of copper is rho = 1.70 Times 10^-8 Ohm m. The wire is tightly wrapped in a coil to make an inductor. (Tightly wrapped means there is no space between each turn...each loop is touching the adjacent loop of the coil. As a visual example, the image on the right shows 8 turns of a tightly wrapped coil.) Each loop of the coil has a radius of 1.20 cm, and the entire length of wire is used to make the coil. What is the total resistance of the length of wire? What is the inductance of the coil? The coil is connected to a battery with an emf of 3.00 V to make a simple circuit. What is the time constant of the circuit? What is the maximum current in the circuit? (What is the current after the circuit has been connected for a long period of time? How much magnetic energy is stored in the inductor in the steady state? Starting from the moment the coil is connected to the battery, how long does it take for the current in the circuit to reach 50% of its maximum value?

Explanation / Answer

when the switch is open

R3 = R4   and R3 and R4 are in parallel , hence current divides between R3 and R4 equally

i3 = i4

since current in R1 is the sum of current in R3 and R4

i1 = i3 + i4

when the switch is closed

R2 , R3 and R4 are in parallel . hence the total resistance of the circuit is smaller which make the current i1 larger than when the switch was open

R2 , R3 and R4 are in parallel and hence current divides equally between them

swicth open                          switch closed

i1                  <                         i1                 since total resistance in closed swicth is smaller

i2                <                          i2               since i2 = 0 when switch was open

i3             >                         i3             since current now divides among three resistance when switch is closed

i4             >                         i4             since current now divides among three resistance when switch is closed