Advertisements
Advertisements
Question
Explain, why is the p.d. between the terminals of a storage battery less when it is supplying current than when it is on open circuit. A battery of e.m.f. 10 volts and internal resistance 2.5 ohms has two resistances of 50 ohms each connected to it. Calculate the power dissipated in each resistance
(a) When they are in series,
(b) When they are in parallel.
In each case calculate the power dissipated in the battery.
Advertisements
Solution
In an open circuit no current is drawn from the cell whereas in closed circuit, an amount of energy is spent in the flow of unit positive charge through the electrolyte of the cell. Thus, the p.d. between the terminals of a storage battery is less when it is supplying current.
Given, emf e = 10 V, internal resistance r = 2.5 Ω
Two external resistances R1 = R2 = 50Ω (= R, say)
(a) When R1 and R2 are connected in series, same current flows through each resisto and hence same power is dissipated in each resistor.
Total resistance of the circuit, Rs=R1 + R2 +r = 50 + 50 + 2.5 = 102.5Ω
Current through each resistor = `"e"/"R"_"s" = 10/102.5 = 0.096"A"`
Power dissipated in each resistor =I2R (0.096)2 (50) = 0.46 watt
(b) When R1 and R2 are connected in parallel, voltage across each resistor is same and hence same power is dissipated in each resistor.
Total resistance of the circuit Rp = `(1/"R"_1 + 1/"R"_2)^-1 + r = 25 + 2.5 = 27.5 Omega`
Current through the circuit, I= `"e"/"R"_"p" = 10/27.5 = 0.36 "A"`
Voltage across each resistor, V = e -Ir= 10 - ( 0.36 x 2.5) = 9.1V
Power dissipated in each resistor P = `"V"^2/"R" = (9.1)^2/50 = 4140.5 "watt"`
APPEARS IN
RELATED QUESTIONS
How can three resistors of resistances 2 Ω, 3 Ω and 6 Ω be connected to give a total resistance of 4 Ω ?
A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B, each of 24 Ω resistances, which may be used separately, in series, or in parallel. What are the currents in the three cases?
Which of the following combinations have the same equivalent resistance between X and Y?
A particular resistance wire has a resistance of 3 ohm per meter. Find the total resistance of three lengths of this wire each 1.5 m long, joined in parallel.
Tick (✓) the correct choice among the following :
Consider two cases of two parallel current carrying conductors. Current in
th e same direction and currents in th e opposi te directions will produce
A cell supplies a current of 1.2 A through two 2Ω resistors connected in parallel. When the resistors are connected in series, if supplies a current of 0.4 A. Calculate the internal resistance and e.m.f of the cell.
State the S.I. unit of electrical resistance and define it.
How does the resistance of a metallic wire depend on the length of wire?
In the figure below, the ammeter A reads 0.3 A. Calculate:
(i) the total resistance of the circuit
(ii) the value of R
(iii) the current flowing through R.
The diagram above is a schematic diagram of a household circuit. The house shown in the above diagram has 5 usable spaces where electrical connections are made. For this house, the mains have a voltage of 220 V and the net current coming from the mains is 22A.
- What is the mode of connection to all the spaces in the house from the mains?
- The spaces 5 and 4 have the same resistance and spaces 3 and 2 have respective resistances of 20Ω and 30Ω. Space 1 has a resistance double that of space 5. What is the net resistance for space 5.
- What is the current in space 3?
- What should be placed between the main connection and the rest of the house’s electrical appliances to save them from accidental high electric current?
