Page 304 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 25] DIRECT-CURRENTCIRCUITS 289

SOLVED PROBLEM 25.2
It is desired to limit the current in a 50- resistor to 10 A when it is connected to a 600-V power source. (a)
How should an auxiliary resistor be connected in the circuit and what should its resistance be? (b) What
is the voltage drop across each resistor?

(a) For a current of 10 A, the total resistance in the circuit should be
V 600 V
R = = = 60
I 10 A
Hence a 10- resistor should be connected in series with the 50- resistor to give a total of 60 .
(b) V 1 = IR 1 = (10 A)(50 ) = 500 V V 2 = IR 2 = (10 A)(10 ) = 100 V

SOLVED PROBLEM 25.3

(a) What is the equivalent resistance of three 5- resistors connected in series? (b) If a potential difference
of 60 V is applied across the combination, what is the current in each resistor? (c) What is the voltage
drop across each resistor?
(a) R = R 1 + R 2 + R 3 = 5 + 5 + 5 = 15
(b) The current in the entire circuit is
V 60 V
I = = = 4A
R 15
Since the resistors are in series, this current flows through each of them.
(c) The voltage drop across each of the resistors is
V = IR = (4A)(5 ) = 20 V

The total voltage drop is 20 V + 20 V + 20 V = 60 V, which is equal to the applied potential difference (see
Fig. 25-2).

20 V 20 V 20 V

5 Ω 5 Ω 5 Ω
I = 4 A
60 V
Fig. 25-2. (From Arthur Beiser, Schaum’s Outline of Basic Mathematics for Electricity and Electronics, 2nd Ed.,
c 1993, The McGraw-Hill Companies. Reproduced with permission of The McGraw-Hill Companies.)

SOLVED PROBLEM 25.4
Two light bulbs, one of 5- and the other of 10- resistance, are connected in series across a potential
difference of 12 V. (a) What is the current in each bulb? (b) What is the voltage across each bulb? (c) What
powers are dissipated by each bulb and by the combination?

The first step is to find the equivalent resistance of the two bulbs, which is
R = R 1 + R 2 = 5 + 10 = 15
(a) The current in the circuit is
V 12 V
I = = = 0.8A
R 15
Since the bulbs are in series, the current in each of them is 0.8 A.