Question

Draw a schematic diagram of a circuit consisting of a battery of 3 cells of
2 V each, a combination of three resistors of 10 ohm , 20ohm and 30 ohm
connected in parallel, a plug key and an ammeter, all connected in series.
Use this circuit to find the value of the following:
(a)
Current through each resistor
(b)
Total current in the circuit
(c)
Total effective resistance of the circuit​

Answer 1

Answer:

(a) i1 = V/R1 = 6 / 10 = 0.6 A

i2 = V / R2 = 6 / 20 = 0.3 A

i3 = V/R3 = 6 / 30 = 0.2 A

(b) Total current, i = 1.1 A

(c) Total effective resistance, R = 5.45 Ohm

Step-by-step explanation:

voltage of each cell = 2 V

number of cells = 3

total voltage of the battery = 3 x 2 = 6 V

R1 = 10 ohm

R2 = 20 ohm

R3 = 30 ohm

All the resistances are in parallel.

So, the equivalent resistance is given by

$\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}$

$\frac{1}{R}=\frac{1}{10}+\frac{1}{20}+\frac{1}{30}$

R = 60 /11 = 5.45 ohm

Total current, i = V / R = 6 / 5.45 = 1.1 A

(a)

Let the current is i1, i2 and i3 in the resistance R1, R2 and R3

Voltage is same across each resistor in parallel combination.

i1 = V/R1 = 6 / 10 = 0.6 A

i2 = V / R2 = 6 / 20 = 0.3 A

i3 = V/R3 = 6 / 30 = 0.2 A

(b) Total current, i = 1.1 A

(c) Total effective resistance, R = 5.45 Ohm