# A circuit contains a battery and four identical resistors arranged as

Thread starter itsagulati Start date Sep 17, Homework Statement The circuit in the drawing contains five identical resistors. Astronuc Staff Emeritus. Science Advisor. So all resistors have same resistance R, but the total resistance is not 5R or 4R. So one has to find the equivalent resistor noting that R3 and R4 are in series, so the combined resistance is 2R. Then that 2R is parallel with R2 and R5. So find the equivalent resistance of that combination.

Last edited: Sep 17, Vijay Bhatnagar. First determine the equivalent resistance of the circuit. R3 and R4 are in series. This 2R, R2 and R5 are in parallel.The circuit in the drawing contains five identical resistors. The V battery delivers 58 W of power to the circuit. What is the resistance R of each resistor? Concept Simulation Determine the power supplied to each of the resistors in the drawing. This is in parallel to R2 and R5.

And this whole thing is in series with R1. We need to remember that in series, current is same potential difference varies. But in parallel, current varies and potential difference is same. Trending News. Trump identifies another hoax: The coronavirus. Hosting shakeup on 'Dancing With the Stars'.

## Series Circuits

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### Resistance of each IDENTICAL resistor?

Still have questions? Get your answers by asking now.Most circuits have more than one component, called a resistor that limits the flow of charge in the circuit. A measure of this limit on charge flow is called resistance. The simplest combinations of resistors are the series and parallel connections illustrated in Figure 1. The total resistance of a combination of resistors depends on both their individual values and how they are connected.

Figure 1. When are resistors in series?

Capacitors in Series and Parallel Explained!

Resistors are in series whenever the flow of charge, called the currentmust flow through devices sequentially. It seems reasonable that the total resistance is the sum of the individual resistances, considering that the current has to pass through each resistor in sequence. This fact would be an advantage to a person wishing to avoid an electrical shock, who could reduce the current by wearing high-resistance rubber-soled shoes. It could be a disadvantage if one of the resistances were a faulty high-resistance cord to an appliance that would reduce the operating current.

Figure 2. Three resistors connected in series to a battery left and the equivalent single or series resistance right. To verify that resistances in series do indeed add, let us consider the loss of electrical power, called a voltage dropin each resistor in Figure 2.

Another way to think of this is that V is the voltage necessary to make a current I flow through a resistance R. The sum of these voltages equals the voltage output of the source; that is.

This equation is based on the conservation of energy and conservation of charge. Thus the energy supplied by the source is qVwhile that dissipated by the resistors is. These energies must be equal, because there is no other source and no other destination for energy in the circuit. Note that the same amount of charge passes through the battery and each resistor in a given amount of time, since there is no capacitance to store charge, there is no place for charge to leak, and charge is conserved.

Now substituting the values for the individual voltages gives. This logic is valid in general for any number of resistors in series; thus, the total resistance R s of a series connection is. Since all of the current must pass through each resistor, it experiences the resistance of each, and resistances in series simply add up. Entering the value of the applied voltage and the total resistance yields the current for the circuit:.

Entering the current and the value of the first resistance yields. In this case, each resistor has the same full current flowing through it. The same values will be obtained. This gives. Note, coincidentally, that the total power dissipated by the resistors is also 7. That is. Power is energy per unit time wattsand so conservation of energy requires the power output of the source to be equal to the total power dissipated by the resistors.

Resistors are in parallel when each resistor is connected directly to the voltage source by connecting wires having negligible resistance. Each resistor thus has the full voltage of the source applied to it. Each resistor draws the same current it would if it alone were connected to the voltage source provided the voltage source is not overloaded.Four resistors and a 6-V battery are arranged as shown in the circuit diagram.

Determine the current through the ohm resistor. You then find the total resistance of the branch which includes the 10 Ohm resistor. At this point a complication arises because we need to know the internal resistance of the 6v battery, which we are not told. However, it is likely that your teacher expects that you will ignore this, and assume that the component marked with a cell symbol is actually intended to be an ideal voltage source with zero or negligible internal resistance. You should point out to your teacher that a circuit symbol exists for an ideal voltage source, and this should be used in cases where it is intended.

Cells or batteries should always be expected to have noticeable internal resistance which can usually not be ignored, and using a cell or battery symbol implies that this is the case. Trending News. Trump identifies another hoax: The coronavirus. Hosting shakeup on 'Dancing With the Stars'. States extend unemployment while Congress debates. Grant Imahara, 'Mythbusters' co-host, dies at All eyes are on Disney World following its reopening. Trump turns focus to Obama after coronavirus question. Praising coach Nick Saban, Trump calls him 'Lou'.

Maxwell wrapped cellphone in tinfoil 'to evade detection'. Answer Save. Still have questions? Get your answers by asking now.A circuit contains a battery and four identical resistors arranged as shown in the diagram below.

If any resistors have potential differences with the same magnitude, state that explicitly. Briefly explain your reasoning. Ranking: Brief explanation: Resistor B is now removed from the circuit, and there is no connection between the wires that were attached to it. The new circuit diagram is shown below. A C D b When resistor B is removed, does the current through resistor A increase, decrease, or remain the same? Increase Decrease Remain the same Briefly explain your reasoning. Questions are typically answered within 1 hour. Q: The teacher then begins introducing pulses with a different wavelength.

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Subscribe Sign in. Operations Management. Chemical Engineering. Civil Engineering. Computer Engineering. Computer Science. Electrical Engineering. Mechanical Engineering.As mentioned in the previous section of Lesson 4two or more electrical devices in a circuit can be connected by series connections or by parallel connections. When all the devices are connected using series connections, the circuit is referred to as a series circuit.

In a series circuit, each device is connected in a manner such that there is only one pathway by which charge can traverse the external circuit. Each charge passing through the loop of the external circuit will pass through each resistor in consecutive fashion. A short comparison and contrast between series and parallel circuits was made in the previous section of Lesson 4.

In that section, it was emphasized that the act of adding more resistors to a series circuit results in the rather expected result of having more overall resistance. Since there is only one pathway through the circuit, every charge encounters the resistance of every device; so adding more devices results in more overall resistance. This increased resistance serves to reduce the rate at which charge flows also known as the current.

Charge flows together through the external circuit at a rate that is everywhere the same. The current is no greater at one location as it is at another location. The actual amount of current varies inversely with the amount of overall resistance. There is a clear relationship between the resistance of the individual resistors and the overall resistance of the collection of resistors. This is the concept of equivalent resistance.

The equivalent resistance of a circuit is the amount of resistance that a single resistor would need in order to equal the overall effect of the collection of resistors that are present in the circuit. For series circuits, the mathematical formula for computing the equivalent resistance R eq is.

The current in a series circuit is everywhere the same. Charge does NOT pile up and begin to accumulate at any given location such that the current at one location is more than at other locations. Charge does NOT become used up by resistors such that there is less of it at one location compared to another. The charges can be thought of as marching together through the wires of an electric circuit, everywhere marching at the same rate. Current - the rate at which charge flows - is everywhere the same. It is the same at the first resistor as it is at the last resistor as it is in the battery. Mathematically, one might write. These current values are easily calculated if the battery voltage is known and the individual resistance values are known.

Using the individual resistor values and the equation above, the equivalent resistance can be calculated. As discussed in Lesson 1the electrochemical cell of a circuit supplies energy to the charge to move it through the cell and to establish an electric potential difference across the two ends of the external circuit. This is to say that the electric potential at the positive terminal is 1. As charge moves through the external circuit, it encounters a loss of 1.

This loss in electric potential is referred to as a voltage drop. It occurs as the electrical energy of the charge is transformed to other forms of energy thermal, light, mechanical, etc. If an electric circuit powered by a 1. There is a voltage drop for each resistor, but the sum of these voltage drops is 1.

This concept can be expressed mathematically by the following equation:. To illustrate this mathematical principle in action, consider the two circuits shown below in Diagrams A and B.

Suppose that you were to asked to determine the two unknown values of the electric potential difference across the light bulbs in each circuit. To determine their values, you would have to use the equation above.

The battery is depicted by its customary schematic symbol and its voltage is listed next to it. Determine the voltage drop for the two light bulbs and then click the Check Answers button to see if you are correct.

Earlier in Lesson 1, the use of an electric potential diagram was discussed. An electric potential diagram is a conceptual tool for representing the electric potential difference between several points on an electric circuit.Post a Comment. Navigation Home Past papers. Question : 4. A circuit contains a battery and four identical resistors arranged as shown in the diagram below.

If any resistors have potential differences with the same magnitude, state that explicitly. Explain your answer. Scoring Guidelines :. Explain correctly why the electric current through R A decreases because of the change in electric current or electrical potential difference in the circuit. Possible answers :. The electrical circuit can be redrawn as follows.

The ranking of electrical potential difference can be presented as follows:. The electric current is decreased from 0.

The electric current is increased from 0. The proportionality coefficient is called the resistance R. When the electrical current is sufficiently high, this can lead to a significant heating effect.

First, a heating of the electrical conductor may increase the temperature of the conductor. Second, the increase in temperature can result in an increase in the length of the conductor. Third, when the temperature of the conductor is being increased, the electrical resistance is also increased, and this can lead to a reduction in the electric current through the conductor.

References :. Ashford, C. The elementary theory of direct current dynamo electric machinery.