Concept explainers
The current in the resistor
Answer to Problem 37P
The net current in
Explanation of Solution
Write the expression for the induced emf.
Here,
Conclusion:
Calculate the emf for the left rod.
Substitute
Here,
Calculate the emf for the sright rod.
Substitute
Here,
Let the current in left loop be
It is given that
Apply Kirchhoff voltage law in left loop.
Apply Kirchhoff voltage law in right loop.
Substitute
Substitute
Further solve for
Substitute
Further solve for
Therefore, current in the left loop is
Substitute
Therefore current in the right loop is
Net current
Substitute
Therefore, the net current in
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Chapter 31 Solutions
Physics for Scientists and Engineers With Modern Physics
- Two resistanceless rails rest 42 cm apart on a 6.6o ramp. They are joined at the bottom by a 0.68 Ω resistor. At the top, a copper bar of mass 0.034 kg (ignore its resistance) is laid across the rails. The whole apparatus is immersed in a vertical 0.35 T field. What is the terminal (steady) velocity of the bar as it slides frictionlessly down the rails?arrow_forwardTwo straight conducting rails form a right angle as shown in the figure. A conducting bar with the specific resistance of 0.125 Q per meter is in contact with the rails. The rails have no X X x xx x * ** X X X X X X X X XX X X X X X X XXX X X X Xx X X X X resistance. The bar starts at the vertex at time t= 0 and moves X X X XX Xy X X X with a constant velocity of 2 m/s parallel to the median of the triangle. Conducting rails and the bar are in a uniform magnetic field with the magnitude of B =0.25 T directed into the page. What is the induced current flowing through the bar x x x x *x x x x and its direction at t = 2 s? (CW: Clockwise, CcW: Counterclockwise looking from above) X x X Xx X X X X X X x xx x x X X X X X X x x x x X X X X X X x X x x X X X X X X x x x x x О 1А, ССW О 2А, СW О 4А, ССW O OA O None of them O 1A, CW O 2 A, CCW O 4A, CWarrow_forwardYou connect a battery, resistor, and capacitor as in (Figure 1), where R = 14.0 Ω and C = 3.00 ×10^-6 F. The switch S is closed at t = 0. When the current in the circuit has magnitude 3.00 A, the charge on the capacitor is 40.0 × 10^−6 C. At what time t after the switch is closed is the charge on the capacitor equal to 40.0 x 10^-6 C? When the current has magnitude 3.00 A, at what rate is energy being stored in the capacitor?arrow_forward
- Q4: Show detailed work and pay attention to the units. There are two different ways to calculate the potential difference across the bar, using the motional EMF expression or Faraday's Law. Show that both methods give the same answer. Use the right hand rule to figure out which end of the bar (A or B) will be at a higher potential due to the motion of the conductor in the field.arrow_forwardTwo straight conducting rails form a right angle as shown in the figure. A conducting bar with the specific resistance of 0.125 N per meter is in contact with the rails. The rails have no X x x x x x x x x X X X X X X X X X X XXXX х х х х х X X XX Xx X X XX resistance. The bar starts at the vertex at time t= 0 and moves x xXx x x xỷ x x x with a constant velocity of 2 m/s parallel to the median of the triangle. Conducting rails and the bar are in a uniform magnetic field with the magnitude of B =0.25 T directed into the page. What is the induced current flowing through the bar x x x x xX x x x x and its direction at t = 2 s ? (CW: Clockwise, CCW: Counterclockwise looking from above) X x X x x X X XX X X X X x x x X X X x x xX x x x X X X X X X X x X X XX x x x x x x x x x X 1А, СCW O A 4А, CW 2A, CW 1А, CW None of them 2 А, СCW 4А, СCWarrow_forwardFor the circuit shown in Fig. Q1(a), the capacitor is initially charged to 3.5 V with polarity shown. compute the time constant, T of the circuit. I = 5.5 mA ↑ R₁ R₂ 2.6 ΚΩ 18.7 ΚΩ Fig. Ql(a) S C = 3.3 uF + 3.5 Varrow_forward
- For the circuit shown in Fig. Q2(b), assuming the switch has been opened for a very long time, when the switch opens at t = 0 s, compute the current i, (t) and voltage v₁ (t) when the switch S₁ is closed. 27 V S iL + VL - L → 158 mH 3.5 mA Fig. Q2(b) 6.6 ΚΩ Rarrow_forwardQI. A capacitor consists of two circular plates of radius a separated by a distance d (assume d a. (A) Use Gauss' Law to find the electric field between the plates as a function of time t, in terms of q(1), a, ɛ, and z. The vertical direction is the k direction. (B)Now take an imaginary flat disc of radius rarrow_forwardFor the circuit shown in Fig. Q1(a), the capacitor is initially charged to 3.5 V with polarity shown. compute the voltage vc(t) and the current ic (t) when the switch (S) is closed. I = 5.5 mA ↑ R₁ R₂ 2.6 ΚΩ • 8.7 ΚΩ Fig. Ql(a) S C = 3.3 uF + 3.5 Varrow_forwardTwo straight conducting rails form a right angle as shown in the figure. A conducting bar with the specific resistance of 0.125 0 per meter is in contact with the rails. The rails have i x x x X X XX x xX X x x x X X XX X X X X X x x x x x no X X x XX X X XX resistance. The bar starts at the vertex at time t= 0 and moves X X X XX Xx x X with a constant velocity of 2 m/s parallel to the median of the triangle. Conducting rails and the bar are in a uniform magnetic field with the magnitude of B =0.25 T directed into the page. What is the induced current flowing through the bar x x ****** and its direction at t 2 s? (CW: Clockwise, CCW: Counterclockwise looking from above) X XX X X X X XX X X XX x x X X x x X x X x X X X X X X XxX x X X x X x x x x x x x x None of them 2A, CW O OA 1A, CCW O 4A, CCW O 4A, CW O 1A, CW 2 A, СCWarrow_forwardd k k S +. AV The circuit in figure consists of two identical parallel metal plates connected by identical metal springs to a 100 V battery. The surface area of one plate is 1778 m². With the switch open, the plates are uncharged, and separated by a distance d = 10 mm. When the switch is closed, the distance between the plates decreases by a factor of half. What is the spring constant, in Newton/meter, for each spring? E, = 9 x 10-12 C² /Nm² a) 160000 b) 20000 c) 10240 d) 2500 e) 1280arrow_forwardIn the figure R₁ = 9.69 kN, R₂ = 15.9 kn, C = 0.379 μF, and the ideal battery has emf ε =20.0 V. First, the switch is closed a long time so that the steady state is reached. Then the switch is opened at time t = 0. What is the current in resistor 2 at t = 3.90 ms? E Number i + Fu R₁ www R₂ с Units Aarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning