Question

Draw a schematic diagram of a circuit consisting of a battery of three cells of 2 V each, a 4

Ω resistor, 8 Ω resistor, and a 12 Ω resistor, and a plug key, all connected in series. [5]

(a)Calculate the current flowing through 4Ω resistor.

(b)Calculate the potential difference across 12Ω resistor.

(c)Calculate the equivalent resistance of the circuit.​

Answer 1

Answer:

a) I=volt/ampere

I=2×3/4=1.5A

b)V=IR

V=1.5×12=18V

c)R=R1+R2+R3

R=4+8+12=24ohms

Answer 2

Answer:

Refer to the attachment for diagram consisting of:

• A battery of three cells 2 V each
• A 4Ω resistor, a 8Ω resistor, a 12Ω resistor
• A plug key, all connected in series.

Solutions for (a), (b) and (c)

To find:-

• Current flowing through 4Ω resistor
• The Potential difference across 12Ω resistor
• The equivalent resistance of the circuit

Solution:-

There are three cells in the battery, each of 2 V so,

→ Potential difference of battery, V = 2 V + 2 V + 2 V = 6 V

Calculating the equivalent resistance of the series circuit

→ R(eq) = 4Ω + 8Ω + 12Ω = 24 Ω

Using the expression for ohm's law

→ V = I R

[ where V is the potential difference, I is current and R is resistance ]

Calculating the current flowing through the whole circuit

→ I = V / R

→ I = 6 / 24

→ I = 1 / 4 = 0.25 A

[In a series combination, all the connected resistors have the same current flowing through them that is equal to the current flowing in the whole circuit.]

Therefore,

• Current flowing through the 4Ω resistor will be 0.25 A
• and, Equivalent resistance of the circuit will be 24 Ω

Now, we need to find the potential difference across 12Ω resistor

[Because In a series combination, all the connected resistors have the same current flowing through them that is equal to the current flowing in the whole circuit.]

so the current through 12Ω resistor will be 0.25 A

Hence, Using Expression for ohm's law

calculating the potential difference (V') through R' = 12Ω resistor

→ V' = I R'

→ V' = 0.25 × 12

→ V' = 3 V

Therefore,

• The potential difference through the 12Ω resistor will be 3 V.

Extra shots:-

• Combined resistance of any number of resistors connected in series is equal to the sum of the individual resistances.

• Sum of potential difference across all the resistances is equal to the voltage of the battery in series, but different potential differences across different resistors.

• The number of resistances in series has the same current flowing through each resistor that is equal to the current flowing in the whole circuit.