Question

two resistors in parallel A of 20 ohms and B of unknown value are connected in series with a third resistor C of 12 ohms. the supply to the circuit is direct current. if the p.d across the end of resistor C is 180v and the power in the complete circuit is 3600w. calculate the following
(i) the value of the unknown resistor
(ii) the current in each resistor
(iii) the circuit voltage

Answer 1

Answer:

i) unknown resistor = 4Ω

ii) Current in resistor A = 3A

Current in resistor B = 12A

Current in resistor C = 15 A

iii) circuit voltage = 240 V

Explanation:

Current through resistor C is

I = 180/12 = 15 A

Since parallel combination of A and B is in series with C

The main current I = 15A

Total power P = VI

Circuit voltage V = P/I

= 3600/15

= 240 V

p.d across parallel combination = 240 - 180 = 60V

Equivalent resistance of parallel combination is

Rp = 60/15 = 4 Ω

Let x be the unknown resistance.

Equivalent resistance of parallel combination is

Rp = 20 x /(20+ x)

∴ 4 = 20x/(20+x)

20 + x = 5x

4x = 20

x = 5 Ω

∴ unknown resistance = 5 Ω

current in resistor A = 60/20 = 3 A

current in resistor B = 60/5 = 12 A

Answer 2

i)Unknown resistor =4Ω

ii) Current in resistor A = 3A

Current in resistor B =12A

Current in resistor C = 15A

iii) Circuit voltage = 240 V

Explanation:

Current through resistor C

is I = 180/12 = 15 A

Since parallel combination of A and B in series with C

The main current I = 15A

Total power P = VI

Circuit voltage V = P/I

= 3600/15

= 240 V

p.d across parallel combination = 240-180 = 60V

Equivalent resistance of parallel combination is

Rp = 60/15 = 4Ω

Let x be the unknown resistance

Equivalent resistance of parallel combination is

Rp = 20x/(20+x)

∴ 4 = 20x/(20+x)

20 + x = 5x

4x = 20

x = 5Ω

∴ unknown resistance = 5Ω

current resistance A = 60/20 = 3 A

current resistance B = 60/5 = 12A