Chapter 12 – Electricity Solutions
Question - 31 : - When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Find the value of the resistance of the resistor
Answer - 31 : - The value of the resistor can be calculated using Ohm’s Law as follows:
Question - 32 : - A battery of 9 V is connected in series with resistors of 0.2 Ω, 0.3 Ω, 0.4 Ω, 0.5 Ω and 12 Ω, respectively. How much current would flow through the 12 Ω resistor?
Answer - 32 : -
In series connection, there is no division of current. The current flowing across all the resistors is the same.
To calculate the amount of current flowing across the resistors, we use Ohm’s law.
But first, let us find out the equivalent resistance as follows:
R = 0.2 Ω + 0.3 Ω + 0.4 Ω + 0.5 Ω + 12 Ω = 13.4 Ω
Now, using Ohm’s law,
The current flowing across the 12 Ω is 0.671 A.
Question - 33 : - How many 176 Ω resistors (in parallel) are required to carry 5 A on a 220 V line?
Answer - 33 : -
Let us consider the number of resistors required as ‘x.’
The equivalent resistance of the parallel combination of resistor R is given by
The number of resistors required is 4.
Question - 34 : - Show how you would connect three resistors, each of resistance 6 Ω, so that the combination has a resistance of (i) 9 Ω, (ii) 4 Ω.
Answer - 34 : - If we connect all the three resistors in series, their equivalent resistor would 6 Ω + 6 Ω + 6 Ω =18 Ω, which is not the desired value. Similarly, if we connect all the three resistors in parallel, their equivalent resistor would be
which is again not the desired value.
We can obtain the desired value by connecting any two of the resistors in either series or parallel.
Case (i)
If two resistors are connected in parallel, then their equivalent resistance is
The third resistor is in series, hence the equivalent resistance is calculated as follows:
R = 6 Ω + 3 Ω = 9 Ω
Case (ii)
When two resistors are connected in series, their equivalent resistance is given by
R = 6 Ω + 6 Ω = 12 Ω
The third resistor is connected in parallel with 12 Ω. Hence the equivalent resistance is calculated as follows:
Answer - 35 : - lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A?
Answer
The resistance of the bulb can be calculated using the expression
P1 = V2/R1
R1 = V2/P1
Substituting the values, we get
Hence, 110 lamps can be connected in parallel.
Question - 36 : - A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B,
Answer - 36 : - each of 24 Ω resistance, which may be used separately, in series, or in parallel. What are the currents in the three cases?
Answer
Case (i) When coils are used separately
Using Ohm’s law, we can find the current flowing through each coil as follows:
9.166 A of current flows through each resistor when they are used separately.
Case (ii) When coils connected in series
The total resistance in the series circuit is 24 Ω + 24 Ω = 48 Ω
The current flowing through the series circuit is calculated as follows:
Therefore, a current of 4.58 A flows through the series circuit.
Case (iii) When coils connected in parallel
When the coils are connected in parallel, the equivalent resistance is calculated as follows:
The current in the parallel circuit is 18.33 A.
Question - 37 : - Compare the power used in the 2 Ω resistor in each of the following circuits:
Answer - 37 : - (i) a 6 V battery in series with 1 Ω and 2 Ω resistors, and (ii) a 4 V battery in parallel with 12 Ω and 2 Ω resistors.
Answer
(i) The potential difference is 6 V and the resistors 1 Ω and 2 Ω are connected in series, hence their equivalent resistance is given by 1 Ω + 2 Ω = 3 Ω. The current in the circuit can be calculated using the Ohm’s law as follows:
Therefore, the power consumed by the 2 Ω is 8 W.
(ii) When 12 Ω and 2 Ω resistors are connected in parallel, the voltage across the resistors remains the same. Knowing that the voltage across 2 Ω resistor is 4 V, we can calculate the power consumed by the resistor as follows:
The power consumed by the 2 Ω resistor is 8 W.
Question - 38 : - Two lamps, one rated 100 W at 220 V, and the other 60 W at 220 V, are connected in parallel to electric mains supply. What current is drawn from the line if the supply voltage is 220 V?
Answer - 38 : -
Since both the bulbs are connected in parallel, the voltage across each of them will be the same.
Current drawn by the bulb of rating 100 W can be calculated as follows:
P = V × I
I = P/V
Substituting the values in the equation, we get
I = 100 W/220 V = 100/220 A
Similarly, the current drawn by the bulb of rating 60 W can be calculated as follows:
I = 60 W/220 V = 60/220 A
Therefore, the current drawn from the line is
Question - 39 : - Which uses more energy, a 250 W TV set in 1 hr, or a 1200 W toaster in 10 minutes?
Answer - 39 : -
The energy consumed by electrical appliances is given by the equation
H = Pt, where P is the power of the appliance and t is the time
Using this formula, the energy consumed by a TV of power ration 250 W, can be calculated as follows:
H = 250 W × 3600 seconds = 9 × 105 J
Similarly, the energy consumed by a toaster of power rating 1200 W is
H = 1200 W × 600 s = 7.2 × 105 J
From the calculations, it can be said that the energy consumed by the TV is greater than the toaster.
Question - 40 : - An electric heater of resistance 8 Ω draws 15 A from the service mains 2 hours. Calculate the rate at which heat is developed in the heater.
Answer - 40 : -
The rate at which the heat develops in the heater can be calculated using the following formula
P = I2 R
Substituting the values in the equation, we get
P = (15A) 2 × 8 Ω = 1800 J/s
The electric heater produces heat at the rate of 1800 J/s