Current Electricity
- A constant voltage of 50 V is maintained between the points A and B of the circuit shown in the figure. The current through the branch CD of the circuit is : Answer: 2. 2.0 A Key idea: C and D are joined by a wire, so they are at the same potential. The circuit becomes two parallel pairs in series... 1
- A wire of resistance R is cut into 8 equal pieces. From these pieces two equivalent resistances are made by adding four of these together in parallel. Then these two sets are added in series. The net effective resistance of the combination is : Answer: 3. R/16 Key idea: cutting a wire into equal parts divides its resistance equally. Each piece has resistance R/8 . Four in parallel g... 1
- The current passing through the battery in the given circuit, is: Answer: 2. 0.5 A Key idea: the middle network is a balanced Wheatstone bridge, so the 6\ Ω resistor carries no current. Points C and D are j... 1
- Two heaters A and B have power rating of 1 kW and 2 kW, respectively. Those two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two cases is: Answer: 3. 2 : 9 Key idea: P=V²/R , so R∝1/P at fixed voltage. Take R_A=2 units (1 kW) and R_B=1 unit (2 kW). Series: R_s=3 , so P_s=V²/3 .... 1
- Choose the correct circuit which can achieve the bridge balance. Answer: 2. circuit (2) Key idea: A Wheatstone bridge is balanced when no current flows through G, i.e. P/Q=R/S . The top arms are 10 Ω and 1... 1
- The terminal voltage of the battery, whose emf is 10 V and internal resistance 1 Ω, when connected through an external resistance of 4 Ω as shown in the figure is : Answer: 4. 8 V Key idea: Terminal voltage V=ε-Ir . Current I=ε/R+r=10/4+1=2 A. V=10-2×1=8 V (equivalently IR=2×4=8 V). Option 4. 1
- A wire of length 'l' and resistance 100 Ω is divided into 10 equal parts. The first 5 parts are connected in series while the next 5 parts are connected in parallel. The two combinations are again connected in series. The resistance of this final com… Answer: 3. 52 Ω Key idea: Each of the 10 equal parts has resistance 100/10=10\ Ω . Five parts in series: 5×10=50\ Ω . Five parts in parallel... 1
- The magnitude and direction of the current in the following circuit is Answer: 3. 0.5 A from A to B through E In the loop the two cells oppose each other (10 V and 5 V), so the net emf is 10-5=5 V. The 10 V cell... 1
- Resistance of a carbon resistor determined from colour codes is (22000±5\%) Ω. The colour of third band must be : Answer: 4. Orange Colour code: first two bands give the digits, the third band gives the power of ten (multiplier), the fourth gives toleran... 1
- The resistance of platinum wire at 0^°C is 2 Ω and 6.8 Ω at 80^°C. The temperature coefficient of resistance of the wire is : Answer: 4. 3×10⁻² ^°C⁻¹ R_t=R₀(1+α t) , so α=R_t-R₀/R₀ t . α=6.8-2/2×80=4.8/160=3×10⁻² ^°C⁻¹ . The answer is 3×10⁻² ^°C⁻¹ . 1
- 10 resistors, each of resistance R are connected in series to a battery of emf E and negligible internal resistance. Then those are connected in parallel to the same battery, the current is increased n times. The value of n is : Answer: 3. 100 Series: R_s=10R , so I₁=E/10R . Parallel: R_p=R/10 , so I₂=10E/R . n=I₂/I₁=10E/R/E/10R=100 . The answer is 100. 1
- If the galvanometer G does not show any deflection in the circuit shown, the value of R is given by : Answer: 4. 100 Ω No deflection means no current in the galvanometer branch, so the potential drop across R equals the 2 V cell. Current in t... 1
- A wheatstone bridge is used to determine the value of unknown resistance X by adjusting the variable resistance Y as shown in the figure. For the most precise measurement of X, the resistances P and Q : Answer: 3. should be approximately equal and are small A Wheatstone bridge is most sensitive when all four arms have comparable resistance,... 1
- A copper wire of length 10 m and radius (10^-2/√(π)) m has electrical resistance of 10 Ω. The current density in the wire for an electric field strength of 10 (V/m) is : Answer: 1. 10⁵ A/m ² Current density is J=σ E=E/ρ , so first find resistivity from R=ρ L/A . A=π r²=π·dfrac10⁻⁴π=10⁻⁴\ m² ρ=RA/L=dfrac10×10⁻... 1
- Two resistors of resistance, 100 Ω and 200 Ω are connected in parallel in an electrical circuit. The ratio of the thermal energy developed in 100 Ω to that in 200 Ω in a given time is : Answer: 3. 2 : 1 In a parallel connection both resistors have the same voltage, so heat produced in a given time depends inversely on resist... 1
- As the temperature increases, the electrical resistance : Answer: 4. increases for conductors but decreases for semiconductors Resistance of a conductor rises with temperature, while that of a semic... 1
- Three resistors having resistances r_1, r_2 and r_3 are connected as shown in the given circuit. The ratio i_3/i_1 of currents in terms of resistances used in the circuit is : Answer: 2. r₂/r₂+r₃ Key idea: r₂ and r₃ are in parallel, and the current i₁ splits in inverse ratio of resistances (current divider). i₃=i₁·... 1
- In a potentiometer circuit a cell of EMF 1.5 V gives balance point at 36 cm length of wire. If another cell of EMF 2.5 V replaces the first cell, then at what length of the wire, the balance point occurs ? Answer: 1. 60 cm Key idea: in a potentiometer, EMF ∝ balancing length. E₂/E₁=l₂/l₁⇒ l₂=36×2.5/1.5=60 cm. Option 1. 1
- The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section and same material is 0.25 Ω. What will be the effective resistance if they are connected in series ? Answer: 4. 4 Ω Key idea: four equal resistors R: parallel gives R/4 , series gives 4R . R/4=0.25\ Ω⇒ R=1\ Ω . In series: 4R=4\ Ω . Option 4. 1
- Column - I gives certain physical terms associated with flow of current through a metallic conductor. Column - II gives some mathematical relations involving electrical quantities. Match Column - I and Column - II with appropriate relations.Column -… Answer: 1. (A)-(R), (B)-(S), (C)-(P), (D)-(Q) (A) Drift velocity v_d=aτ=eE/mτ : R. (B) Resistivity ρ=E/J : S. (C) From ρ=m/ne²τ , relaxation... 1
- A charged particle having drift velocity of 7.5×10^-4 m s^-1 in an electric field of 3×10^-10 V m^-1, has a mobility in m^2 V^-1 s^-1 of : Answer: 2. 2.5×10⁶ Mobility is drift velocity per unit electric field: μ=v_d/E . μ=frac7.5×10⁻⁴3×10⁻¹⁰=2.5×10⁶\ m²V⁻¹s⁻¹ Answer: option 2. 1
- The color code of a resistance is given below :(figure: colour bands Yellow, Violet, Brown, Gold)The values of resistance and tolerance, respectively, are : Answer: 4. 470 Ω , 5% Four-band colour code: first two bands are digits, the third is the multiplier, the fourth is tolerance. Yellow = 4, V... 1
- Which of the following graph represents the variation of resistivity (ρ) with temperature (T) for copper ? Answer: 3. graph (3) For a metal like copper, resistivity rises with temperature because lattice vibrations scatter electrons more: ρ=ρ₀[1+α... 1
- A resistance wire connected in the left gap of a metre bridge balances a 10 Ω resistance in the right gap at a point which divides the bridge wire in the ratio 3 : 2. If the length of the resistance wire is 1.5 m, then the length of 1 Ω of the resist… Answer: 2. 1.0×10⁻¹ m Metre bridge balance: X/10=l/100-l=3/2 . X=15\ Ω This 15 Ω is the resistance of the whole 1.5 m wire. Length per ohm:... 1