Potential Dividers (CIE AS Physics)

A battery is connected in series with resistors P and Q, as shown in Fig 1.1.

The resistance of P is 7.5 Ω. The resistance of Q is constant. A variable resistor of resistance R is connected in parallel with Q.

The current I from the battery is changed by varying R from 5 Ω to 20 Ω. The variation with R of I is shown in Fig 1.2.

Use Fig 1.2 to state and explain the variation of the p.d. across resistor P as R is decreased. Numerical values are not required.

For R = 7.0 Ω, calculate the p.d. between points Y and Z.

Show that the resistance of Q is 95 Ω.

State and explain qualitatively how the power provided by the battery changes as the resistance R is decreased.

When the resistance of R₁ is 6.5 Ω, the voltage across it is 7.0 V.

Show that the resistance of R₂ is 16 Ω.

The resistors are replaced with identical filament lamps A and B and the battery is connected in parallel to a linear potentiometer XY, as shown in Fig 1.2.

Fig 1.2

The lamps each have the same I–V characteristic shown in Fig. 1.3.

Fig 1.3

When the slider of the potentiometer is at its midpoint, as shown in Fig. 1.2, the current I in the battery is 4.12 A.

Determine the current in lamp B.

Calculate the total resistance in the circuit.

The slider of the potentiometer in (c) is moved to end X. State and explain the effect on the current of lamps A and B.

A battery of negligible internal resistance is connected to a thermistor, a switch X and two fixed resistors, as shown in Fig. 1.1.

Resistor R₁ has resistance 8.0 kΩ and resistor R₂ has resistance 12.0 kΩ. When switch X is open, the potential difference across R₂ is 18 V. 

Show that the e.m.f of the battery is 30 V.

Switch X is now closed. The current in the battery is 1.94 A. 

Calculate the resistance of the LDR.

The switch X in the circuit in (a) remains closed. The light intensity on the LDR increases. 

By reference to the current in the battery, state and explain the effect, if any, of the increase in light intensity on the power produced by the battery.

The light intensity on the LDR decreases. 

State and explain what happens to the potential difference across R₁.

A circuit is set up as shown in Fig. 1.1 below: 

Fig. 1.1

The cells in Fig. 1.1 have negligible internal resistance. The cell at the top has an e.m.f. of 5 V and the cell at the bottom has an e.m.f. of 6 V.

 is a variable resistor with a resistance that varies between 0 and 10 Ω, and  and  are fixed resistors with a resistance of 10 Ω and 30 Ω respectively. 

Initially,  is set such that its resistance is 0 Ω. 

By labelling the direction of current on Fig. 1.1, write down the relationship between three currents ,   and  at the junction between and .

Determine the current through the resistor .

State and explain what happens to the potential difference across  as the resistance of  is gradually increased from zero.

Calculate the current flowing through each resistor when R₁ is set to a resistance of 10 Ω.

Fig. 1.1 shows a potentiometer in action. The wire in the potentiometer is represented by a fixed resistor of resistance 10 Ω and the sliding contact C can move from one end of the wire (at position P) to the other end of the wire (position Q). This allows the output potential difference (p.d.) to be varied. The potentiometer is in series with another fixed resistor of 5 Ω. 

Fig. 1.1

This circuit is powered by a 9 V power supply and is used to supply a variable potential difference to another circuit. 

Sketch a graph on the axes provided in Fig. 1.2 to show how the supplied potential difference V varies as the moving contact C is moved from position P to position Q.

Fig. 1.2

Sketch a graph on the axes provided in Fig. 1.2 to show how the supplied potential difference V varies as the moving contact C is moved from position P to position Q.

Potential divider circuits generally comprise of two or more resistors in series with each other. 

Some potential divider circuits have multiple branches connected in parallel, such as that shown in Fig. 1.3: 

Fig. 1.3

Show that the potential difference between X and Y, V_OUT , is 1 V.

Fig. 1.4 shows another potential divider circuit which includes a thermistor with resistance R. 

Fig. 1.4

The battery has an EMF of 12 V, with negligible internal resistance. At room temperature, the resistance of the thermistor is 5 kΩ.

Calculate the current in the battery at room temperature.