Question

For the circuit shown in the figure, find the current through and the potential difference across each resistor.

What is the current through the 3 Ω resistor?

What is the current through the 4 Ω resistor? 

What is the potential difference across the 3 Ω resistor.

What is the potential difference across the 4 Ω resistor?

What is the potential difference across the 48 Ω resistor?

What is the current through the 48 Ω resistor?

What is the potential difference across the 16 Ω resistor?

What is the current through the 16 Ω resistor?

Answer 1

Answer 2

4 , 16 and 48 are connected in parallel, consider Re as their effective resistance,
1 / Re = 1 / 4 + 1 / 16 + 1 / 48
= 16 / 48 = 1 / 3
Re = 3

Re and 3 are in series, the equivalent resistance of the circuit is,
R = Re + 3
= 3 + 3
= 6
----------------------------
Current through the circuit, I = V / R
= 12 / 6
= 2 A
Voltage across 3 resistor, V3 = 2 * 3 = 6 V

Since 4 , 16 and 48 are connected in parallel, the voltage across them are same, which is 6 V
Current through 4 = 6 / 4 = 1.5 A
Current through 16 = 6 / 16 = 0.375 A
Current through 48 = 6 / 48 = 0.125 A
----------------------------------------------------
i) 3 , voltage = 6 V, current = 2 A
ii) 4 , voltage = 6 V, current = 1.5 A
iii) 16 , voltage = 6 V, current = 0.375 A
iv) 48 , voltage = 6 V, current = 0.125 A