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 , 20 and 30
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
Answers
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}}
R
1
=
R
1
1
+
R
2
1
+
R
3
1
\frac{1}{R}=\frac{1}{10}+\frac{1}{20}+\frac{1}{30}
R
1
=
10
1
+
20
1
+
30
1
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