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#current calculation

37 public questions tagged with this topic.

A parallel plate capacitor has a time-varying charge such that \( \frac{dQ}{dt} = 1.2 \, \text{A} \). What is the displa

**Charging capacitor** conduction current in wires equals displacement current between plates because dQ/dt = I_c = ε₀ A dE/dt = ε₀ dΦ_E/dt = I_d, preserving charge conservation, magnetic field between plates due to I_d, same as that due to conduction current. In a capacitor, the displacement current i_d equals the conduction current in the connecting wires, so i_d = (dQ/dt) = 1.2 A . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 1.2 A, illustrating EM wave transverse nature and Maxwell's displacement current concept.

Ref: NCERT > Physics Book > Electromagnetic Waves > Displacement Current and Ampere-Maxwell Law

A circuit has a \( 10 \, \text{V} \) battery with \( 1 \, \Omega \) internal resistance and two resistors \( 5 \, \Omega

**Conductivity** σ = 1/ρ = n e² τ/m (S/m), τ relaxation time, m electron mass. Resistivity deviation at high fields occurs when τ depends on E or n changes due to impact ionization, breaking Ohm's law, seen in varistors, gas discharge. Parallel resistance: (1/R_p) = (1/5) + (1/10) = (2 + 1/10) = (3/10) ⇒ R_p = (10/3) ≈ 3.33 Ω . Total resistance: Rtₒtₐl = 1 + 3.33 = 4.33 Ω . Current: I = (ε/Rtₒtₐl) = (10/4.33) ≈ 2.31 A . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel, V = ε

Ref: NCERT > Physics Book > Current Electricity > Potentiometer, Conductivity and Special Cases

A copper wire of cross-sectional area \( 5 \times 10^{-7} \, \text{m}^2 \) carries a current of \( 1 \, \text{A} \). If

**Conductivity** σ = 1/ρ = n e² τ/m (S/m), τ relaxation time, m electron mass. Resistivity deviation at high fields occurs when τ depends on E or n changes due to impact ionization, breaking Ohm's law, seen in varistors, gas discharge. Drift speed: v_d = (I/n e A) . Substitute: v_d = (1/8.5 × 10²⁸ × 1.6 × 10⁻¹⁹ × 5 × 10⁻⁷) . Calculate: v_d = (1/6.8 × 10³) ≈ 1.47 × 10⁻⁴ m/s . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel, V = ε - I r and P = I²R,

Ref: NCERT > Physics Book > Current Electricity > Potentiometer, Conductivity and Special Cases

A copper wire of length \( 2 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) carries a curr

**Unbalanced bridge** has potential difference between galvanometer nodes, current direction determined by which node higher potential, i.e., if R₁/R₂ > R₃/R₄, left node higher, current flows one way, else opposite. Galvanometer deflection indicates imbalance magnitude. Drift speed is given by v_d = (I/n e A) . Given: I = 2 A , n = 8.5 × 10²⁸ m⁻³ , e = 1.6 × 10⁻¹⁹ C , A = 2 × 10⁻⁶ m² . Substitute: v_d = (2/8.5 × 10²⁸ × 1.6 × 10⁻¹⁹ × 2 × 10⁻⁶) . Calculate: v_d = (2/2.72 × 10⁴) = 7.35 × 10⁻⁵ m/s . Applying I = n e

Ref: NCERT > Physics Book > Current Electricity > Wheatstone Bridge and Meter Bridge

A \( 21 \, \text{V} \) battery with negligible internal resistance is connected to a cubical network of 12 resistors, ea

**Meter bridge** uses uniform wire of length 1 m, balance length l gives R_unknown = R_known·l/(100-l). Principle same as Wheatstone, with wire resistances proportional to lengths, allowing unknown resistance determination from length ratio. Equivalent resistance: Rₑq = (5/6) R = (5/6) × 2.5 = (12.5/6) ≈ 2.08 Ω . Total current: I = (V/Rₑq) = (21/(12.5/6)) = 21 × (6/12.5) = 10.08 A ≈ 10.1 A . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel, V = ε - I r and P = I²R, evaluation yields 10.1 A,

Ref: NCERT > Physics Book > Current Electricity > Wheatstone Bridge and Meter Bridge

Two cells of emf \( 5 \, \text{V} \) and \( 9 \, \text{V} \) with internal resistances \( 1 \, \Omega \) and \( 2 \, \Om

**Total voltage drop** across series equals source voltage because loop rule Σ V = ε, with internal resistance r included V = ε - I r. For 4 Ω,8 Ω,16 Ω parallel, 1/R_p =1/4+1/8+1/16=7/16, R_p=16/7≈2.29 Ω, then total resistance with internal 3 Ω is 5.29 Ω, current I=18/5.29≈3.4 A. Equivalent emf: εₑq = 5 + 9 = 14 V . Total resistance: Rtₒtₐl = 1 + 2 + 7 = 10 Ω . Current: I = (εₑq/Rtₒtₐl) = (14/10) = 1.4 A . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel, V = ε

Ref: NCERT > Physics Book > Current Electricity > Kirchhoff's Laws and Combination of Resistors

A copper wire of cross-sectional area \( 2.5 \times 10^{-7} \, \text{m}^2 \) carries a current of \( 0.85 \, \text{A} \)

**Resistivity temperature variation** ρ_t = ρ₀[1+α(T-T₀)], α ≈4×10⁻³ /°C for copper, 1.7×10⁻⁴ /°C for nichrome. Given R=60 Ω at 30°C, α=1.7×10⁻⁴ /°C, T=330°C, ΔT=300°C, R_t=60[1+1.7×10⁻⁴×300]=60×1.051=63.06 Ω, modest increase for nichrome due to small α. Drift speed: v_d = (I/n e A) . Substitute: v_d = (0.85/8.5 × 10²⁸ × 1.6 × 10⁻¹⁹ × 2.5 × 10⁻⁷) . Calculate: v_d = (0.85/3.4 × 10³) ≈ 2.5 × 10⁻⁴ m/s . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel, V = ε - I r and P = I²R, evaluation yields 2.5 × 10⁻⁴ m/s, consistent

Ref: NCERT > Physics Book > Current Electricity > Temperature Dependence of Resistance and Resistivity

A circuit has a \( 10 \, \text{V} \) battery with \( 1 \, \Omega \) internal resistance and three resistors \( 2 \, \Ome

**Kirchhoff's loop rule** (energy conservation) states algebraic sum of potential differences around closed loop zero, Σ ε - Σ I R =0, ensures total voltage drop across series resistors equals source emf. Junction rule (charge conservation) Σ I_in = Σ I_out ensures current continuity. Parallel resistance: (1/R_p) = (1/2) + (1/4) + (1/8) = (4 + 2 + 1/8) = (7/8) ⇒ R_p = (8/7) ≈ 1.14 Ω . Total resistance: Rtₒtₐl = 1 + 1.14 = 2.14 Ω . Total current: I = (ε/Rtₒtₐl) = (10/2.14) ≈ 4.67 A . Voltage across parallel: V = I R_p = 4.67 × 1.14 ≈ 5.33 V

Ref: NCERT > Physics Book > Current Electricity > Kirchhoff's Laws and Combination of Resistors

A circuit has a \( 12 \, \text{V} \) battery with \( 3 \, \Omega \) internal resistance and two resistors \( 6 \, \Omega

**Kirchhoff's loop rule** (energy conservation) states algebraic sum of potential differences around closed loop zero, Σ ε - Σ I R =0, ensures total voltage drop across series resistors equals source emf. Junction rule (charge conservation) Σ I_in = Σ I_out ensures current continuity. Parallel resistance: (1/R_p) = (1/6) + (1/3) = (1 + 2/6) = (3/6) = 0.5 ⇒ R_p = 2 Ω . Total resistance: Rtₒtₐl = 3 + 2 = 5 Ω . Current: I = (ε/Rtₒtₐl) = (12/5) = 2.4 A . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel,

Ref: NCERT > Physics Book > Current Electricity > Kirchhoff's Laws and Combination of Resistors

A circuit has a \( 9 \, \text{V} \) battery with \( 1 \, \Omega \) internal resistance and two resistors \( 5 \, \Omega

**Total voltage drop** across series equals source voltage because loop rule Σ V = ε, with internal resistance r included V = ε - I r. For 4 Ω,8 Ω,16 Ω parallel, 1/R_p =1/4+1/8+1/16=7/16, R_p=16/7≈2.29 Ω, then total resistance with internal 3 Ω is 5.29 Ω, current I=18/5.29≈3.4 A. Parallel resistance: (1/R_p) = (1/5) + (1/3) = (3 + 5/15) = (8/15) ⇒ R_p = (15/8) = 1.875 Ω . Total resistance: Rtₒtₐl = 1 + 1.875 = 2.875 Ω . Current: I = (ε/Rtₒtₐl) = (9/2.875) ≈ 3.13 A . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT],

Ref: NCERT > Physics Book > Current Electricity > Kirchhoff's Laws and Combination of Resistors

A \( 36 \, \text{V} \) battery with negligible internal resistance is connected to a cubical network of 12 resistors, ea

**Series combination** R_eq = R₁+R₂+..., same current I through each, voltage divides proportionally V_i = I R_i. Parallel combination 1/R_p = 1/R₁+1/R₂+..., same voltage V across each, current divides inversely, equivalent R_p = (R₁ R₂)/(R₁+R₂) for two resistors. Equivalent resistance: Rₑq = (5/6) R = (5/6) × 6 = 5 Ω . Total current: I = (V/Rₑq) = (36/5) = 7.2 A . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel, V = ε - I r and P = I²R, evaluation yields 7.2 A,

Ref: NCERT > Physics Book > Current Electricity > Kirchhoff's Laws and Combination of Resistors

A \( 10 \, \Omega \) resistor dissipates \( 25 \, \text{W} \) of power. What is the current through it?

**Power dissipation** in resistor converts electrical energy to heat, P = V²/R inversely proportional to R for fixed V, directly proportional for fixed I. For battery with internal r, power wasted internally = I² r, useful power = I² R, efficiency η = R/(R+r). Power: P = I² R . Rearrange: I = √((P/R)) . Substitute: I = √((25/10)) = √(2.5) ≈ 1.58 A . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel, V = ε - I r and P = I²R, evaluation yields 1.58 A,

Ref: NCERT > Physics Book > Current Electricity > Electrical Power, Energy and Heating Effect