The circuit shown consists of four different resistors and a battery. You do not know the strength of the battery or the values of any of the four resistances. Which expressions listed will be equal to the emf (?) across the battery? Note that for the choices, ?Vi represents the magnitude of the difference in potential across resistance Ri for all i = 1, 2, 3, 4. A. ? = ?V1 + ?V2 B. ? = ?V1 + ?V3 C. ? = ?V2 + ?V3 D. ? = ?V1 + ?V2 + ?V3 E. ? = ?V1 + ?V2 + ?V3 + ?V4 F. ? = ?V1 + ?V4 G. ? = ?V4 H. ? = ?V2 + ?V4 I. ? = ?V3 + ?V4 a. G, H and I b. Only E c. Only G d. Only D e. A, B, and G
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The emf (ε) across the battery is equal to the total potential difference across the entire circuit. Show more…
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Three resistors R1 = 82.6 ̴, R2 = 21.9 ̴, R3 = 70.0 ̴, and two batteries ε1 = 40.0 V, and ε2 = 359 V are connected as shown in the diagram below. (a) What current flows through R1, R2, and R3? I1 = A I2 = A I3 = A (b) What is the absolute value of the potential difference across R1, R2, and R3? |ΔVR1| = V |ΔVR2| = V |ΔVR3| = V
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Assume the resistance values are $R_{1}=2400 \Omega, R_{2}=1400 \Omega, R_{3}=4500 \Omega,$ and $R_{4}=6000 \Omega,$ and the battery emfs are $\varepsilon_{1}=1.5 \mathrm{V}$ and $\varepsilon_{2}=3.0 \mathrm{V},$ unless stated otherwise. Use Kirchhoff's rules to analyze the circuit in Figure P19.56. a. Let $I_{1}$ be the branch current though $R_{1}, I_{2}$ be the branch current through $R_{2}$, and $I_{3}$ be the branch current through $R_{3} .$ Write Kirchhoff's loop rule relation for a loop that travels through battery 1, resistor 1, and resistor 3. b. Write Kirchhoff's loop rule relation for a loop that travels through battery $2,$ resistor $2,$ and resistor 3. c. Apply Kirchhoff's junction rule to the junction at $A$ to get a relation between the three branch currents. d. You should now have three equations and three unknowns $\left(I_{1}, I_{2}, \text { and } I_{3}\right) .$ Solve for the three branch currents.
Electric Currents and Circuits
DC Circuits: Batteries, Resistors, and Kirchhoff’s Rules
Assume the resistance values are $R_{1}=2400 \Omega, R_{2}=1400 \Omega, R_{3}=4500 \Omega,$ and $R_{4}=6000 \Omega,$ and the battery emfs are $\varepsilon_{1}=1.5 \mathrm{V}$ and $\varepsilon_{2}=3.0 \mathrm{V},$ unless stated otherwise. Use the approach from Problems 50 and 51 to analyze the circuit in Figure P19.52. What is the current through the battery and resistor $R_{1}$ ? Hint: First redraw the circuit so that the parallel and series resistor combinations are more obvious.
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