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#1. (a) [1 point] Explain why the resistance of a conductor increases with temperature. (b) [5 points] For the following circuit Vs = 12 V, R1 = 3.3 k?, R2 = R3 = 2.2 k?, R4 = 4.7 k?. (i) Find the current through each resistor of the network. (ii) Show that the power dissipated by the resistors is equal to the power supplied by the battery. #2. [6 points] Four 10 ?F capacitors are connected in a network in such a way that the equivalent capacitance becomes 6 ?F. (a) Find how the capacitors are connected in the network. (b) If a 12 V battery in connected across the network, (i) Find the voltage drop across each capacitor in the network. (ii) Determine the total energy stored in the capacitors in equilibrium. #3. (a) [1 point] Ampere's law is analogous to Gauss' law in electrostatics. Gauss' law deals with a closed surface, whereas Ampere's law deals with a closed loop. Why? Explain. (b) [5 points] A long solenoid having a radius of 5 cm and 200 turns per meter is surrounded by another coil of 120 turns and radius 8 cm. If the current in the long solenoid changes at a rate of 20 A/s, find the induced EMF in the second coil while the field is changing.

          #1. (a) [1 point] Explain why the resistance of a conductor increases with temperature.
(b) [5 points] For the following circuit Vs = 12 V, R1 = 3.3 k?, R2 = R3 = 2.2 k?, R4 = 4.7 k?.
(i) Find the current through each resistor of the network.
(ii) Show that the power dissipated by the resistors is equal to the power supplied by the battery.
#2. [6 points] Four 10 ?F capacitors are connected in a network in such a way that the equivalent capacitance becomes 6 ?F.
(a) Find how the capacitors are connected in the network.
(b) If a 12 V battery in connected across the network,
(i) Find the voltage drop across each capacitor in the network.
(ii) Determine the total energy stored in the capacitors in equilibrium.
#3. (a) [1 point] Ampere's law is analogous to Gauss' law in electrostatics. Gauss' law deals with a closed surface, whereas Ampere's law deals with a closed loop. Why? Explain.
(b) [5 points] A long solenoid having a radius of 5 cm and 200 turns per meter is surrounded by another coil of 120 turns and radius 8 cm. If the current in the long solenoid changes at a rate of 20 A/s, find the induced EMF in the second coil while the field is changing.

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#1. (a) [1 point] Explain why the resistance of a conductor increases with temperature.
(b) [5 points] For the following circuit Vs = 12 V, R1 = 3.3 k?, R2 = R3 = 2.2 k?, R4 = 4.7 k?.
(i) Find the current through each resistor of the network.
(ii) Show that the power dissipated by the resistors is equal to the power supplied by the battery.
#2. [6 points] Four 10 ?F capacitors are connected in a network in such a way that the equivalent capacitance becomes 6 ?F.
(a) Find how the capacitors are connected in the network.
(b) If a 12 V battery in connected across the network,
(i) Find the voltage drop across each capacitor in the network.
(ii) Determine the total energy stored in the capacitors in equilibrium.
#3. (a) [1 point] Ampere's law is analogous to Gauss' law in electrostatics. Gauss' law deals with a closed surface, whereas Ampere's law deals with a closed loop. Why? Explain.
(b) [5 points] A long solenoid having a radius of 5 cm and 200 turns per meter is surrounded by another coil of 120 turns and radius 8 cm. If the current in the long solenoid changes at a rate of 20 A/s, find the induced EMF in the second coil while the field is changing.

Added by Erika J.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Luis Rios

04/29/2021

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Step 1: Calculate the total resistance of the circuit by combining resistors in series and parallel. Show more…

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#1. (a) [1 point] Explain why the resistance of a conductor increases with temperature. (b) [5 points] For the following circuit Vs = 12 V, R1 = 3.3 kΩ, R2 = R3 = 2.2 kΩ, R4 = 4.7 kΩ. (i) Find the current through each resistor of the network. (ii) Show that the power dissipated by the resistors is equal to the power supplied by the battery. #2. [6 points] Four 10 μF capacitors are connected in a network in such a way that the equivalent capacitance becomes 6 μF. (a) Find how the capacitors are connected in the network. (b) If a 12 V battery in connected across the network, (i) Find the voltage drop across each capacitor in the network. (ii) Determine the total energy stored in the capacitors in equilibrium. #3. (a) [1 point] Ampere's law is analogous to Gauss' law in electrostatics. Gauss' law deals with a closed surface, whereas Ampere's law deals with a closed loop. Why? Explain. (b) [5 points] A long solenoid having a radius of 5 cm and 200 turns per meter is surrounded by another coil of 120 turns and radius 8 cm. If the current in the long solenoid changes at a rate of 20 A/s, find the induced EMF in the second coil while the field is changing.

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Transcript

00:01 In this problem, we have two resistors, r1, which is equal to r, and r2, which is equal to 2 times r.

00:10 And they're connected to a battery.

00:12 And we want to figure out which one dissipates more power depending on how they're connected to the battery.

00:19 The first, in part a, would be when they are in series, and in part b, when they are in parallel.

00:25 So there's a few key things we need to know.

00:27 So when the resistors are connected in series, that means they have the same current flowing through them.

00:37 So the current will be the same in the first resistor and in the second resistor.

00:45 For part b, when they're in parallel, that means each resistor has the same voltage across it.

00:53 So the voltage will be the same for resistors 1 and resistors 2.

01:01 And part a, when they are in series, since we're looking at current, then the equation we can use in series will be power is equal to current square times the resistance.

01:19 And for parallel, since we're looking at voltage, the voltage being the key thing, then the equation here for power will be power is equal to the voltage squared divided by the resistance.

01:38 So in part a, again here the resistors are connected in series, so they have the same current.

01:46 So if you look at the equation for power for the first one, power will be 1 will equal current squared times r1.

01:58 And again, they have the same currents here when they're in series.

02:02 And then the second register, p2, we have i squared times r2...

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