Question

In the circuit the resistors R1
R2, and R3, have the values 5 ohm, 10 ohm,30 ohm , respectively, which have
been connected to a battery of 12 V. Calculate the total circuit
resistance.
​

Answer 1

The equivalent resistance of the 5Ω, 10Ω, 30Ω resistors connected in parallel is
R
p
​

1
​
=
5
1
​
+
10
1
​
+
30
1
​

=
30
6+3+1
​
=
30
10
​

∴R
p
​
=3Ω
∴, the total resistance of the given circuit is 3 Ohms.
The total current can be calculated using the Ohm's law as the value of voltage (V) is already given.
using Ohm's law
Voltage=Current×Resistance
⇒I=
R
V
​
=
3
12
​
=4A
Current through each resistor can be calculated by applying Ohm's law given that the voltage of the circuit and the individual resistances of each resistor is already given.
Current through 5Ω resistor =
R
V
​
=
5
12
​
=2.4A
Current through 10Ω resistor =
R
V
​
=
10
12
​
=1.2A
Current through 30Ω resistor =
R
V
​
=
30
12
​
=0.4A