(a) Three resistors 1 W, 2 W, and 3 W are combined in series. Whatis the total resistance of the combination? (b) If the combination is connected to a battery of emf 12 V andnegligible internal resistance, obtain the potential drop acrosseach resistor.
(a)
It is given that there are three resistors of 1 Ω , 2 Ω and 3 Ω resistances combined
in series.
The total resistance for the series combination is,
R = R 1 + R 2 + R 3
Substitute the values.
R = 1 + 2 + 3 R = 6 Ω
Thus, the value of total resistance is 6 Ω .
(b)
It is given that the battery has an emf of 12 V .
The formula for the emf is,
E = I R ,
Substitute the value of E and R in the above equation.
12 = I × 6 I = 2 A
The potential drop across R 1 is,
V 1 = I R 1
Substitute the value of I and R 1 in the above equation.
V 1 = 2 × 1 V 1 = 2 V
The potential drop across resistor R 2 is V 2 = I R 2
Substitute the value of I and R 2 in the above equation.
V 2 = 2 × 2 V 2 = 4 V
The potential drop across R 3 is,
V 3 = I R 3
Substitute the value of I and R 3 in the above equation.
V 3 = 2 × 3 V 3 = 6 V
Thus, the value of potential drop across resistors is 2 V , 4 V and 6 V .
(a)
It is given that there are three resistors of
in series.
The total resistance for the series combination is,
Substitute the values.
Thus, the value of total resistance is
(b)
It is given that the battery has an emf of
The formula for the emf is,
Substitute the value of
The potential drop across
Substitute the value of
The potential drop across resistor
Substitute the value of
The potential drop across
Substitute the value of
Thus, the value of potential drop across resistors is
