#galvanometer

Wheatstone Bridge and Meter Bridge

A Wheatstone bridge with \( R_1 = 7 \, \Omega \), \( R_2 = 14 \, \Omega \), \( R_3 = 21 \, \Omega \), \( R_4 = 42 \, \Om

**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. Check balance: (R₁/R₂) = (7/14) = 0.5 , (R₃/R₄) = (21/42) = 0.5 . Bridge is balanced. Since balanced, I_g = 0 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 0 A,

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Wheatstone Bridge and Meter Bridge

A Wheatstone bridge with \( R_1 = 8 \, \Omega \), \( R_2 = 16 \, \Omega \), \( R_3 = 12 \, \Omega \), \( R_4 = 24 \, \Om

**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. Check balance: (R₁/R₂) = (8/16) = 0.5 , (R₃/R₄) = (12/24) = 0.5 . Bridge is balanced. Since balanced, I_g = 0 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 0 A,

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Wheatstone Bridge and Meter Bridge

In a Wheatstone bridge, when the bridge is balanced, what is the potential difference across the galvanometer?

**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. At balance, the potential at the two junctions connected to the galvanometer is equal (due to the ratio condition R₁ / R₂ = R₃ / R₄ ), so the potential difference across the galvanometer is zero, and no current flows through it. 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

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Wheatstone Bridge and Meter Bridge

In a Wheatstone bridge with \( R_1 = 30 \, \Omega \), \( R_2 = 60 \, \Omega \), \( R_3 = 15 \, \Omega \), and \( R_4 = 3

**Wheatstone bridge balance** condition R₁/R₂ = R₃/R₄, R₄ = R₂ R₃/R₁, when galvanometer current zero, potentials at midpoints equal. At balance, no current through galvanometer, enabling precise resistance measurement independent of source voltage. Apply Kirchhoff’s rules. Let currents be I₁ (AB), I₂ (AD), I_g (BD). Junction B: I₁ = I_g + I₄ , Junction D: I₂ = I_g + I₃ . Loop BADB: 30 I₁ + 10 I_g - 60 I₂ = 0 ⇒ 3 I₁ + I_g - 6 I₂ = 0 . Loop BCDB: 60 (I₁ - I_g) - 10 I_g - 15 (I₂ + I_g) = 0 ⇒ 4 I₁ - 2

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Wheatstone Bridge and Meter Bridge

In a Wheatstone bridge, what is the condition for no current to flow through the galvanometer?

**Wheatstone bridge balance** condition R₁/R₂ = R₃/R₄, R₄ = R₂ R₃/R₁, when galvanometer current zero, potentials at midpoints equal. At balance, no current through galvanometer, enabling precise resistance measurement independent of source voltage. No current flows when the bridge is balanced, i.e., R₁ / R₂ = R₃ / R₄ , making the potentials at the galvanometer’s nodes equal, so the potential difference across it is zero. 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 Ratio of resistances in opposite a

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Wheatstone Bridge and Meter Bridge

A Wheatstone bridge with \( R_1 = 6 \, \Omega \), \( R_2 = 12 \, \Omega \), \( R_3 = 9 \, \Omega \), \( R_4 = 18 \, \Ome

**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. Check balance: (R₁/R₂) = (6/12) = 0.5 , (R₃/R₄) = (9/18) = 0.5 . Bridge is balanced. Since balanced, I_g = 0 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 0 A,

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Wheatstone Bridge and Meter Bridge

A Wheatstone bridge with \( R_1 = 5 \, \Omega \), \( R_2 = 10 \, \Omega \), \( R_3 = 15 \, \Omega \), \( R_4 = 30 \, \Om

**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. Check balance: (R₁/R₂) = (5/10) = 0.5 , (R₃/R₄) = (15/30) = 0.5 . Bridge is balanced. Since balanced, I_g = 0 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 0 A,

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Wheatstone Bridge and Meter Bridge

A Wheatstone bridge with \( R_1 = 12 \, \Omega \), \( R_2 = 24 \, \Omega \), \( R_3 = 18 \, \Omega \), \( R_4 = 36 \, \O

**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. Check balance: (R₁/R₂) = (12/24) = 0.5 , (R₃/R₄) = (18/36) = 0.5 . Bridge is balanced. Since balanced, I_g = 0 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 0 A,

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Wheatstone Bridge and Meter Bridge

A Wheatstone bridge with \( R_1 = 9 \, \Omega \), \( R_2 = 18 \, \Omega \), \( R_3 = 12 \, \Omega \), \( R_4 = 24 \, \Om

**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. Check balance: (R₁/R₂) = (9/18) = 0.5 , (R₃/R₄) = (12/24) = 0.5 . Bridge is balanced. Since balanced, I_g = 0 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 0 A,

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Wheatstone Bridge and Meter Bridge

A Wheatstone bridge with \( R_1 = 10 \, \Omega \), \( R_2 = 20 \, \Omega \), \( R_3 = 15 \, \Omega \), \( R_4 = 30 \, \O

**Wheatstone bridge balance** condition R₁/R₂ = R₃/R₄, R₄ = R₂ R₃/R₁, when galvanometer current zero, potentials at midpoints equal. At balance, no current through galvanometer, enabling precise resistance measurement independent of source voltage. Check balance: (R₁/R₂) = (10/20) = 0.5 , (R₃/R₄) = (15/30) = 0.5 . Bridge is balanced. Since balanced, I_g = 0 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 0 A,

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Wheatstone Bridge and Meter Bridge

A Wheatstone bridge with \( R_1 = 16 \, \Omega \), \( R_2 = 32 \, \Omega \), \( R_3 = 24 \, \Omega \), \( R_4 = 48 \, \O

**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. Check balance: (R₁/R₂) = (16/32) = 0.5 , (R₃/R₄) = (24/48) = 0.5 . Bridge is balanced. Since balanced, I_g = 0 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 0 A,

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Wheatstone Bridge and Meter Bridge

A Wheatstone bridge with \( R_1 = 4 \, \Omega \), \( R_2 = 8 \, \Omega \), \( R_3 = 6 \, \Omega \), \( R_4 = 12 \, \Omeg

**Wheatstone bridge balance** condition R₁/R₂ = R₃/R₄, R₄ = R₂ R₃/R₁, when galvanometer current zero, potentials at midpoints equal. At balance, no current through galvanometer, enabling precise resistance measurement independent of source voltage. Check balance: (R₁/R₂) = (4/8) = 0.5 , (R₃/R₄) = (6/12) = 0.5 . Bridge is balanced. Since balanced, I_g = 0 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 0 A,

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