Principle of the Potential Divider

Question 1

there is a circuit with a 12V battery and two resistors in series, 6 and 18 ohms. what is the current in the circuit

Answer 1

• I = V / R
• R = 6 + 18 = 24
• 12 / 24 = 0.5A

Question 2

what is the potential difference across the resistor with 6 ohms and the one with 18 ohms

Answer 2

• V = IR
• 6 x 0.5 = 3V
• 18 X 0.5 = 9V

Question 3

how does this support the conservation of energy

Answer 3

3 + 9 = 12V the battery supplies

Question 4

what do you notice about the ratios between the resistance and potential difference across each resistor

Answer 4

the ratio between resistance and pd for both is 2 : 1

Question 5

what do you notice about the ratio between the resistance of the two resistors as well as the ratio between their pds

Answer 5

• the ratio between the 6 and 18 one is 1 : 3

- the ratio between the 3 and 9V is also 1 : 3

Question 6

what has happened to the resistance from the battery when it has come across the two resistors

Answer 6

• they have divided the potential difference of 12V into 3 and 9 across them
• this arrangement is called a potential divider

Question 7

how could you have used the knowledge of ratios to calculate the pd across both resistors

Answer 7

• you know that the ratio between resistance and pd is going to be proportional
• and you know the ratio between the 6 and 18 ohm resistors is 1 : 3
• meaning the divided pd will also be 1 : 3
• 1 + 3 = 4
• 12 / 4 = 3
• 3 x 1 = 3V for the 6 ohm
• 3 x 3 = 9V for the 18 ohm

Question 8

there is a circuit with a 7.5V battery and two resistors, 6 and 12 ohms in series. what is the potential difference across the 6 ohm resistor

Answer 8

• ratio of 6 to 12 = 1 : 2
• 1 + 2 = 3
• 7.5V / 3 = 2.5
• 1 x 2.5 = 2.5V

Question 9

a filament lamp with 6 ohms of resistance is placed in parallel to the 6 ohm resistor. what is the potential difference across the lamp

Answer 9

it is not just 2.5V

• you should treat the resistor and lamp as one resistor
• 1 / (1/6 + 1/6) = 3 ohms
• using the initial method to find current, 3 + 12 = 15 ohms
• I = V / R so 7.5 / 15 = 0.5A
• V = IR of 0.5 x 3 = 1.5V

Question 10

what is the current in the lamp

Answer 10

• you calculated that the total current is 0.5A
• and the bulb in parallel
• so 0.5 / 2 = 0.25A

Question 11

what two formulae can be derived if no current is taken by the output

Answer 11

• I = V2 / R2

- and I = V / R1 + R2

Question 12

if they both equal I, what are those two equations’ relationship

Answer 12

V2 / R2 = V / R1 + R2

Question 13

what would that equation look like if you wanted V2 on its own

Answer 13

• V2 = V R2 / R1 + R2
• or V2 = V x (R2 / R1 + R2)
  or similarly V1 = V x (R1 / R1 + R2)

Question 14

if you have a three terminal resistor, where you change the resistance of R1 and R2 by sliding a slider, which would increase one and simultaneously decrease the other, what does this mean about how the total resistance is calculated

Answer 14

R1 + R2 always = total R

Question 15

as the sliding contact gets moved up, R2 gets larger and R1 gets smaller. how could the previous equation with the Vs in it have something added to it in order to this distinction to be able to be made

Answer 15

V(out) = V(in) x R2 / R1 + R2

Question 16

how will V(out) change as the slider is moved up

Answer 16

it will progressively get larger

Question 17

what would V(out) equal if the slider was right at the top and why

Answer 17

it would = V(in)

Question 18

what would V(out) equal if the slider was at the very bottom and why

Answer 18

• it would be 0
• as it being at the bottom means that R2 = 0
• and if it does then R2 / R1 + R2 is 0 / R1 + 0 which is 0
• and V(in) x 0 is 0 so V(out) is 0