Question

A circuit is made of two $1.5 \mathrm{V}$ batteries and three light bulbs as shown in Figure 19.83. When the switch is closed and the bulbs are glowing, bulb 1 has a resistance of $10 \Omega,$ bulb 2 has a resistance of $40 \Omega,$ bulb 3 has a resistance of $30 \Omega$, and the copper connecting wires have ncgligible resistance. You can also ncglect the internal resistance of the batteries. (a) Make a copy of the circuit diagram. With the switch open, indicate the approximate surface charge with +'s and -'s on your diagram. (b) With the switch open, find the potential differences $V_{B}-V_{C}$ and $V_{D}-V_{K}$. (c) After the switch is closed and the steady state is established, the currents through bulbs $1,2,$ and 3 are $I_{1}, I_{2},$ and $I_{3},$ respectively. Write loop and node equations that could be solved to determine these three unknown currents, but do not solve the equations. Label on the diagram what current directions, loops, and nodes you are using, and explain which equation is which. In order to learn about the general approach, do not use equations for series and parallel resistance in this problem. (You can use these equations to check your work.) (d) In terms of the unknown currents $I_{1}$ $I_{2},$ and $I_{3},$ what is the potential difference $V_{C}-V_{F}$ (with the switch closed $) ?(\mathbf{e})$ In terms of the unknown currents $I_{1}, I_{2},$ and $I_{3},$ how much power is delivered by the batteries (with the switch closed $) ?(f)$ Solve your equations and give values for $I_{1}, I_{2},$ and $I_{3} \cdot(\mathbf{g})$ How many electrons leave the battery at location $N$ every second? (h) What is the numerical value of $V_{C}-V_{F} ?$ (i) What is the numerical value of the power delivered by the batteries? (j) The tungsten filament in the $40 \Omega$ bulb is $8 \mathrm{mm}$ long and has a cross-sectional area of $2 \times 10^{-10} \mathrm{m}^{2} .$ How big is the electric field inside this metal filament?

          A circuit is made of two $1.5 \mathrm{V}$ batteries and three light bulbs as shown in Figure 19.83.
When the switch is closed and the bulbs are glowing, bulb 1 has a resistance of $10 \Omega,$ bulb 2 has a resistance of $40 \Omega,$ bulb 3 has a resistance of $30 \Omega$, and the copper connecting wires have ncgligible resistance. You can also ncglect the internal resistance of the batteries. (a) Make a copy of the circuit diagram. With the switch open, indicate the approximate surface charge with +'s and -'s on your diagram. (b) With the switch open, find the potential differences $V_{B}-V_{C}$ and $V_{D}-V_{K}$. (c) After the switch is closed and the steady state is established, the currents through bulbs $1,2,$ and 3 are $I_{1}, I_{2},$ and $I_{3},$ respectively. Write loop and node equations that could be solved to determine these three unknown currents, but do not solve the equations. Label on the diagram what current directions, loops, and nodes you are using, and explain which equation is which. In order to learn about the general approach, do not use equations for series and parallel resistance in this problem. (You can use these equations to check your work.) (d) In terms of the unknown currents $I_{1}$ $I_{2},$ and $I_{3},$ what is the potential difference $V_{C}-V_{F}$ (with the switch closed $) ?(\mathbf{e})$ In terms of the unknown currents $I_{1}, I_{2},$ and $I_{3},$ how much power is delivered by the batteries (with the switch closed $) ?(f)$ Solve your equations and give values for $I_{1}, I_{2},$ and $I_{3} \cdot(\mathbf{g})$ How many electrons leave the battery at location $N$ every second? (h) What is the numerical value of $V_{C}-V_{F} ?$ (i) What is the numerical value of the power delivered by the batteries?
(j) The tungsten filament in the $40 \Omega$ bulb is $8 \mathrm{mm}$ long and has a cross-sectional area of $2 \times 10^{-10} \mathrm{m}^{2} .$ How big is the electric field inside this metal filament?

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