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Apply the junction rule at point a shown below.

The figure shows a circuit with three horizontal branches and two vertical branches. The first horizontal branch has voltage source ε subscript 1 of 24 V and internal resistance 0.1 Ω with right positive terminal. The second horizontal branch has voltage source ε subscript 2 of 48 V and internal resistance 0.5 Ω with right positive terminal and resistor R subscript 2 of 40 Ω with right current I subscript 2. The third horizontal branch has voltage source ε subscript 3 of 6 V and internal resistance 0.05 Ω with left positive terminal. The first and second branches are connected on the left through resistor R subscript 1 of 5 Ω with upward current I subscript 1 and on the right through R subscript 5 of 20 Ω. The second and third branch are connected on the left through resistor R subscript 3 of 78 Ω with upward current I subscript 3 and on the right through voltage source ε subscript 4 of 36 V and internal resistance 0.2 Ω with upward positive terminal.
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Apply the loop rule to Loop akledcba in the preceding problem.

E 2 I 2 r 2 I 2 R 2 + I 1 R 5 + I 1 r 1 E 1 + I 1 R 1 = 0

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Find the currents flowing in the circuit in the preceding problem. Explicitly show how you follow the steps in the Problem-Solving Strategy: Series and Parallel Resistors .

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Consider the circuit shown below. (a) Find the current through each resistor. (b) Check the calculations by analyzing the power in the circuit.

The positive terminal of voltage source of 20 V and internal resistance 5 Ω is connected to two parallel branches. The first branch has resistors R subscript 1 of 15 Ω and R subscript 3 of 10 Ω. The second branch has resistors R subscript 2 of 10 Ω and R subscript 4 of 15 Ω. The two branches are connected in the middle using resistor R subscript 5 of 5 Ω.

a. I = 1.17 A , I 1 = 0.50 A , I 2 = 0.67 A , I 3 = 0.67 A , I 4 = 0.50 A , I 5 = 0.17 A ;
b. P output = 23.4 W , P input = 23.4 W

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A flashing lamp in a Christmas earring is based on an RC discharge of a capacitor through its resistance. The effective duration of the flash is 0.250 s, during which it produces an average 0.500 W from an average 3.00 V. (a) What energy does it dissipate? (b) How much charge moves through the lamp? (c) Find the capacitance. (d) What is the resistance of the lamp? (Since average values are given for some quantities, the shape of the pulse profile is not needed.)

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A 160 - μ F capacitor charged to 450 V is discharged through a 31.2 -k Ω resistor. (a) Find the time constant. (b) Calculate the temperature increase of the resistor, given that its mass is 2.50 g and its specific heat is 1.67 kJ/kg · ° C , noting that most of the thermal energy is retained in the short time of the discharge. (c) Calculate the new resistance, assuming it is pure carbon. (d) Does this change in resistance seem significant?

a. 4.99 s; b. 3.87 °C ; c. 3.11 × 10 4 Ω ; d. No, this change does not seem significant. It probably would not be noticed.

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Challenge problems

Some camera flashes use flash tubes that require a high voltage. They obtain a high voltage by charging capacitors in parallel and then internally changing the connections of the capacitors to place them in series. Consider a circuit that uses four AAA batteries connected in series to charge six 10-mF capacitors through an equivalent resistance of 100 Ω . The connections are then switched internally to place the capacitors in series. The capacitors discharge through a lamp with a resistance of 100 Ω . (a) What is the RC time constant and the initial current out of the batteries while they are connected in parallel? (b) How long does it take for the capacitors to charge to 90 % of the terminal voltages of the batteries? (c) What is the RC time constant and the initial current of the capacitors connected in series assuming it discharges at 90 % of full charge? (d) How long does it take the current to decrease to 10 % of the initial value?

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Consider the circuit shown below. Each battery has an emf of 1.50 V and an internal resistance of 1.00 Ω . (a) What is the current through the external resistor, which has a resistance of 10.00 ohms? (b) What is the terminal voltage of each battery?

The circuit shows three parallel branches. The first and second branch both have two voltage sources ε with positive terminals upward and internal resistances r. The third branch has a resistor R.

a. 0.273 A; b. V T = 1.36 V

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Analog meters use a galvanometer, which essentially consists of a coil of wire with a small resistance and a pointer with a scale attached. When current runs through the coil, the pointer turns; the amount the pointer turns is proportional to the amount of current running through the coil. Galvanometers can be used to make an ammeter if a resistor is placed in parallel with the galvanometer. Consider a galvanometer that has a resistance of 25.00 Ω and gives a full scale reading when a 50 - μ A current runs through it. The galvanometer is to be used to make an ammeter that has a full scale reading of 10.00 A, as shown below. Recall that an ammeter is connected in series with the circuit of interest, so all 10 A must run through the meter. (a) What is the current through the parallel resistor in the meter? (b) What is the voltage across the parallel resistor? (c) What is the resistance of the parallel resistor?

The figure shows an ammeter with resistance R subscript M connected across resistor R subscript P with current of 10 A.
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Questions & Answers

Maxwell's stress tensor is
Ami Reply
Yes
doris
neither vector nor scalar
Anil
if 6.0×10^13 electrons are placed on a metal sphere of charge 9.0micro Coulombs, what is the net charge on the sphere
Rita Reply
18.51micro Coulombs
ASHOK
Is it possible to find the magnetic field of a circular loop at the centre by using ampere's law?
Rb Reply
Is it possible to find the magnetic field of a circular loop at it's centre?
Rb Reply
yes
Brother
The density of a gas of relative molecular mass 28 at a certain temperature is 0.90 K kgmcube.The root mean square speed of the gas molecules at that temperature is 602ms.Assuming that the rate of diffusion of a gas in inversely proportional to the square root of its density,calculate the density of
Gifty Reply
A hot liquid at 80degree Celsius is added to 600g of the same liquid originally at 10 degree Celsius. when the mixture reaches 30 degree Celsius, what will be the total mass of the liquid?
Gifty
Under which topic
doris
what is electrostatics
Yakub Reply
Study of charges which are at rest
himanshu
Explain Kinematics
Glory Reply
Two equal positive charges are repelling each other. The force on the charge on the left is 3.0 Newtons. Using your notes on Coulomb's law, and the forces acting on each of the charges, what is the force on the charge on the right?
Nya Reply
Using the same two positive charges, the left positive charge is increased so that its charge is 4 times LARGER than the charge on the right. Using your notes on Coulomb's law and changes to the charge, once the charge is increased, what is the new force of repulsion between the two positive charges?
Nya
A mass 'm' is attached to a spring oscillates every 5 second. If the mass is increased by a 5 kg, the period increases by 3 second. Find its initial mass 'm'
Md Reply
a hot water tank containing 50,000g of water is heated by an electric immersion heater rated at 3kilowatt,240volt, calculate the current
Samuel Reply
what is charge
Aamir Reply
product of current and time
Jaffar
Why always amber gain electrons and fur loose electrons? Why the opposite doesn't happen?
Mohammed Reply
A closely wound search coil has an area of 4cm^2,1000 turns and a resistance of 40ohm. It is connected to a ballistic galvanometer whose resistance is 24 ohm. When coil is rotated from a position parallel to uniform magnetic field to one perpendicular to field,the galvanometer indicates a charge
Palak Reply
Using Kirchhoff's rules, when choosing your loops, can you choose a loop that doesn't have a voltage?
Michael Reply
how was the check your understand 12.7 solved?
Bysteria Reply
Practice Key Terms 3

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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