Question

Two resistances in parallel , A of 2o ohms and B
of unknown value, are then connected in series with a third resistance C of 12 m.
ne supply to the circuit is direct
current. If the potential difference across the
ends of resistance is 180V and power in
the complete circuit is 3600w, calculate
(1)The value of resistance B,
(2) The current in each resistance,
(3) The circuit voltage​

Answer 1

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