10.2 DC: Potential Dividers

In the circuit below, a voltmeter of resistance R_V and an ammeter of resistance R_A are used to measure the resistance R of the fixed resistor.

Which condition is necessary for an accurate value to be obtained for R ?

A power supply and a solar cell are compared using the potentiometer circuit shown.

The e.m.f. produced by the solar cell is measured on the potentiometer.

 The potentiometer wire PQ is 100.0 cm long and has a resistance of 5.00 Ω. The power supply has an e. m .f. of 2.000 V, and the solar cell has an e .m. f. of 5.00 mV.

Which resistance R must be used so that the galvanometer reads zero when PS = 40.0 cm ?

The diagrams show the same cell, ammeter, potentiometer and fixed resistor connected in different ways.

The distance d between the sliding contact and a particular end of the potentiometer is varied. The current measured is then plotted against the distance d.

 For which two circuits will the graphs be identical ?

In the circuit shown, XY is a length L of uniform resistance wire. R₁ and R₂ are unknown resistors. J is a sliding contact that joins the junction of R₁ and R₂ to points on XY through a small signal lamp S.

To determine the ratio    of the potential differences across R₁ and R₂, a point is found on XY at which the lamp is off. This point is at a distance x from X.

 What is the value of the ratio    ?

In the potentiometer circuit below, the moveable contact is placed at N on the bare wire XY, such that the galvanometer shows zero deflection.

The resistance of the variable resistor is now increased.

 What is the effect of this increase on the potential difference across the wire XY and on the position of the moveable contact for zero deflection ?

 

	Potential difference across XY	Position of moveable contact
A B C D	increases increases decreases decreases	nearer to X nearer to Y nearer to X nearer to Y

The graph below shows how resistance R of a thermistor varies during part of a day.

 

The thermistor is connected to the potential divider circuit as shown.

At 0730, an output of 6.0 V is required.

 What value of the variable resistor should be set at this time?

The contact is connected one at a time to points X, Y and Z to test the circuit. The lamps do not light up because lamp L is blown.

Which of the following are the readings of the voltmeter when the contact is connected to each of the points?

 

	X	Y	Z
A B C D	12 V 8 V 12 V 8 V	8 V 8 V 12 V 12 V	4 V 0 V 0 V 4 V

A potential divider has a constant supply of 6.0 V, as shown in the diagrams.

 Which circuit will provide a potential difference between X and Y that can be varied between zero and 3.0 V ?

The resistance R of an unknown resistor is compared with a fixed 100 Ω resistor using the circuit as shown in the diagram.

 The balance length l is 30.0 cm and 48.3 cm when P is connected to Q and R, respectively. 

The length of the wire XY is 100 cm and has a resistance of 40 Ω. The two cells E₁ and E_2, have negligible internal resistances.

 What is the value of resistance R ?

In the circuit below, P is a potentiometer of total resistance 10 Ω and Q is a fixed resistor of resistance 10 Ω. The battery has an e .m f. of 4.0 V and negligible internal resistance. The voltmeter has a very high resistance .

The slider on the potentiometer is moved from X to Y, and a graph of voltmeter reading V is plotted against slider position.

 Which graph would be obtained ?

In the circuit below, the ammeter reading is I, and the voltmeter reading is V.

When the switch is closed, which row describes what happens to I and V?

 

	I	V
A B C D	decreases increases increases stays the same	decreases to zero stays the same decreases to zero increases

The diagram shows a potential divider connected to a 9.0 V supply of negligible internal resistance.

What range of voltages can be obtained between P and Q?

A potential divider consisting of resistors of resistance R₁ and R₂ is connected to an input potential difference of V₀ and gives an output p .d. of V.

What is the value of V ?

A potential divider consists of resistors of resistance R₁ and R₂ connected in series across a source of potential difference V₀. The potential difference across R₁ is V _out .

Which changes to R₁ and R₂ will increase the value of V _out ?

 

	R1	R2
A B C D	doubled doubled halved halved	doubled halved doubled halved

A 12 V battery is in series with an ammeter, a 2 W fixed resistor and a 0 – 10 W variable resistor. High-resistance voltmeters P and Q are connected across the variable resistor and the fixed resistor, respectively, as shown.

The resistance of the variable resistor is changed from its maximum value to zero.

Which graph shows the variation with current of the voltmeter readings?

A potentiometer is used as shown to compare the e. m. f. s of two cells.

The balance points for cells X and Y are 0.70 m and 0.90 m respectively.

 If the e. m .f. of cell X is 1.1 V, what is the e .m. f. of cell Y ?

A potential divider circuit consists of fixed resistors of resistance 2.0 Ω and 4.0 Ω connected in series with a 3.0 Ω resistor fitted with a sliding contact. These are connected across a battery of e. m .f. 9.0 V and zero internal resistance, as shown.

What are the maximum and the minimum output voltages of this potential divider circuit?

 

	Maximum voltage / V	Minimum  voltage / V
A B C D	4.0 5.0 9.0 9.0	2.0 2.0 0 2.0

A battery with e.m.f. E and internal resistance r is connected in series with an external variable resistor.

The value of the external resistance R is slowly increased from zero.

 Which statement is correct ? (Ignore any temperature effects.)