For the bridge shown Z_{1} = 200 ∠20° Ω, Z_{2} = 150 ∠30° Ω and Z_{3} = 300 ∠30° Ω. What is the value of Z_{4 }so that the bridge is balanced?
At bridge balance condition,
Z_{1} Z_{4 }= Z_{2} Z_{3}
⇒ 200 ∠20° Z_{4} = 150 ∠30° 300 ∠30°
⇒ Z_{4} = 225 ∠20° Ω
A simple slide wire potentiometer is used for measurement of current in the circuit. The voltage drop across a standard resistor of 0.6Ω is balanced at 60 cm. The magnitude of current if the standard cell of 4V is balanced at 50 cm is ______ (in A)
Standard cell of 4 V is balanced at 50 cm.
The voltage drop across 60 cm
The working current through the circuit is,
In the bridge circuit shown in figure when then the voltmeter reads
At bridge balance condition
(2R) (X_{c}) = (2R) (R)
Given that,
at this condition, bridge is balanced
Hence the voltmeter reading is 0 V.
A resistance potentiometer has a total resistance of 4 kΩ and is rated 10W. If the range of potentiometer is 0 to 200 mm. then its sensitivity is _______ (in V/mm)
R = 4 kΩ
P = 10 W
We know that.
The potentiometer range is 0 to 200 mm.
A length of cable was tested for insulation resistance using loss of charge method. A capacitance formed by sheath of cable of 300 PF is found to have drop in voltage from 300 V to 100 V in 120 seconds. Calculate the insulation resistance of the cable in MΩ
Given that = C = 300 pF
V_{1} = 300 V
V_{2} = 100 V
t = 120 S
Calculate the value of effective resistance (in Ω) at a supply frequency of 100 Hz. (C_{4 }= 2 μF)
Under balance condition
Separate and equating real and imaginary part.
Find the excitation frequency (in Hz) in the Ac Bridge shown in figure under balance condition. The circuit component values are given as
R_{1} = 100 kΩ,
R_{3} = R_{4} = 100 kΩ,
C_{1} = 2 C_{2} = 10 nF
under bridge balance condition,
Given that, R_{3} = R_{4}
(1 + jωR_{1}C_{1})(1 + jωR_{2}C_{2}) = jωC_{1}R_{2}
1 + jωR_{1}C_{1 }+ jωR_{2}C_{2 }− ω^{2}R_{1}R_{2}C_{1}C_{2 }= jωC_{1}R_{2}
By comparing real parts on both sides,
By comparing imaginary parts on both sides,
The Schering bridge shown in figure has the following constant R_{1} = 1.5 kΩ, C_{1} = 0.4 μF, R_{2} = 3 kΩ and C_{3} = 0.4 μF at frequency 1 kHz. The dissipation factor is_______
Given, R_{1} = 1.5 kΩ
C_{1} = 0.4 μF
R_{2} = 3 kΩ
C_{3} = 0.4 μF
f = 1 kHz
We know that,
and the unknown capacitance
Dissipation factor
= 2πfC_{x}R_{x}
= 2π × 1 × 10^{3} × 0.2 × 10^{6} × 3 × 10^{3}
= 3.77
The AC bridge is supplied with a source of frequency 5 kHz as shown in the figure. If the bridge is balanced at R_{1} = 4 R_{2} and C_{3} = 20 μF, the value of unknown capacitor C_{x} is _____ (in μF)
At bridge balanced condition,
By comparing imaginary part,
The dc potentiometer shown in the figure has working current of 10 mA with switch S open. Let R_{g} + R_{1} = 100Ω. The galvanometer G can only detect currents greater than 10 μA. The maximum percentage error in the measurement of the unknown e.m.f. E_{x} as calculated from the slider position shown is closest to
Given that, when the switch is open.
I_{W} = 10 mA
⇒ R_{x} = 50 Ω.
Length of R_{x} = 5m.
Resistance across 3m = 30 Ω
Resistance across 2m = 20 Ω
Voltage across 20 Ω = 20 × 10 × 10^{3} = 0.2 V
Errors in the reading are due to R_{g} and R_{1}.
Error = voltage drop across R_{g} and R_{1}
= I_{g} (R_{g} + R_{1})
= 10 × 10^{6} (100) = 1 mV
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