A steady current is set up in a metallic wire of a non-uniform cross-section. How is the rate of flow K of electrons related to the area of cross-section A?
When a wire of uniform cross-section, having resistance $R$, is bent into a complete circle, the resistance between any two of diametrically opposite points will be
A
$\frac{R}{8}$
B
$\frac{R}{2}$
C
$4 R$
✓
$\frac{R}{4}$
Answer
Correct option: D.
$\frac{R}{4}$
$\frac{R}{4}$
Hint:
It becomes two resistors each of (d) $\frac{R}{2}$, connected in parallel.
n resistances, each of r Ω, when connected in parallel give an equivalent resistance of R Ω. If these resistances were connected in series, the combination would have resistance in horns equal to
✓
$n^2 R$
B
$\frac{R}{n^2}$
C
$\frac{R}{n}$
D
$nR$
Answer
Correct option: A.
$n^2 R$
$n^2 R$
Hint:
Resistance in parallel combination, $R =\frac{r}{n} \Rightarrow r = Rn$
Resistance in series combination, $R^{\prime}=n r=n^2 R$
A battery of emf 10 V and internal resistance 3 Ω is connected to a resistor. The current in the circuit is. 0.5 A. The terminal voltage of the battery when the circuit is closed is
A milliammeter of range 10 mA has a coil of resistance 1 Ω. To use it as a voltmeter of range 10 V, the resistance that must be connected in series with it is
✓
999 Ω
B
1000 Ω
C
9 Ω
D
99 Ω
Answer
Correct option: A.
999 Ω
$999 \Omega$
Hint:
$
R =\frac{V}{I_g}- R _{ g }=\frac{10}{10 \times 10^{-3}}-1=999 \Omega
$
$
A 10 m long wire of resistance 20 Ω is connected in series with a battery of emf 3 V and a resistance of 10 Ω. The potential gradient along the wire in volt per meter is
A
6.02
B
0.1
✓
0.2
D
1.2
Answer
Correct option: C.
0.2
0.2 Hint:
Potential difference across the wire $=\frac{20}{3} \times 3=2 V$
Potential gradient $=\frac{v}{l}=\frac{2}{10}=0.2 V / m$
A copper wire of length $2 m$ and area of cross-section $1.7 \times 10^{-6} m ^2$ has a resistance of $2 \times 10^{-2} \Omega$. The resistivity of copper is
When current I flows through a wire, the drift velocity of the electrons is v. When current 21 flows through another wire of the same material having double the length and area of cross-section, the drift velocity of the electrons will be-
A
$\frac{v}{4}$
B
$\frac{v}{2}$
✓
$v$
D
$2 v$
Answer
Correct option: C.
$v$
$v$
Hint:
$
V _{ d }=\frac{1}{n A e} ; v _{ d }^{\prime}=\frac{2 I}{(2 A) n e}= v _{ d }
$