Question

Four resistors and a 6-V battery are arranged as shown in the circuit diagram. (a) Determine the equivalent resistance for this circuit. (b) What is the smallest current and in which resistors) does it pass? (c) What is the largest potential difference and across which resistor(s) is it applied?

Answer 1

(a) The equivalent resistance for this circuit is 12 Ω

(b) The smallest current will pass through 60 ohms resistor and the value is 0.222 A.

(c) The largest potential difference across the resistor is 10 V.

How to calculate the equivalent resistance of the circuit?

(a) The equivalent resistance for this circuit is calculated by applying the following method;

1/R = 1/60 + 1/30

1/R = (1 + 2) / 60

1/R = 3/60

R = 60 / 3

R = 20

R = 20Ω + 10Ω

R = 30 Ω

1/R = 1/30 + 1/20

1/R = (2 + 3)/60

1/R = 5/60

R = 60 / 5

R = 12 Ω

(b) The current through the circuit is calculated as;

I = V/R

I = 6 / 12

I = 0.5 A

The smallest current will pass through 60 ohms resistor;

between 10 ohms , 30 ohms and 60 ohms

= 20/30 x 0.5 A

= 0.333 A

in 60 ohms;

= (60 / 90) x 0.333 A

= 0.222 A

(c) The largest potential difference across the resistor is;

V = 20 Ω x 0.5 A

= 10 V